History of the Seminar

Speaker: Lisa Berry, UCSB

Title: Effective Strategies for Teaching Math: Beyond the Usual Formulas

Have you ever felt frustrated that your students "just aren't getting it," despite your best efforts to explain mathematical concepts and work through problems? This talk will explore underlying causes that may explain why students in a typical math course/section tend to fall short of mastering the course learning goals. We will investigate alternative teaching strategies that can help students to succeed, including the importance of context, attention to units, and active learning approaches. Participants will be invited to join in the conversation and can expect to leave with new ideas for their teaching.

Speaker: Marcy Robertson, The University of Western Ontario

Title: An introduction to Operad theory.

Abstract: An operad is an abstraction of a family of composable functions of $n$ variables. Indeed, the most fundamental example of an operad is the endomorphism operad $End_X :=\{ Map(X^n,X)\}_{n≥1}$. Where, given a set or topological space $X$, \{Map(X^n,X)\}$ means the set or space of functions from the$n$-fold product of $X$ with itself to $X$, together with the operations $Map(X^n,X)\times Map(X^m,X)\rightarrow Map(X^{n+m−1},X)$ given, for $1 ≤ i ≤ n$, by $(f\circ g)(x_1, ... , x_{m+n−1}) = f (x_1, ... , x_{i−1}, g(x_i , ... , x_{i+m−1}), x_{i+m}, ...).$ Operads were originally studied as a tool in algebraic topology, but the theory of operads has recently received new inspiration from homological algebra, algebraic geometry, and especially string field theory and deformation quantization. The purpose of this talk is to introduce the basic definitions and examples of operad theory and to describe as many applications as time permits.

Work-life balance: a workshop for women in science

Presented by Tracy Blois, Ph.D., President of the Los Angeles - Ventura Chapter of the Association for Women in Science (AWIS)

The UCSB Women in Science and Engineering (WISE) organization is putting on this exciting workshop for women in science. Take a look at the flyer. Make sure to RSVP.

Note the Special Time and Location:
Wednesday, February 15, 7 - 9 p.m.
1001 Engineering Science Bldg. (ESB), UCSB

Speaker: Ayaka Shimizu, Osaka City University Advanced Mathematical Institute (OCAMI)

Title: A game based on knot theory

Abstract: We introduce "Region Select" which is a game (or game app) using knot theory. In this game we consider a knot projection on a display whose crossings have "lamps" which can be turned on or off by clicking on the region bordering it. The goal of this game is to light up all of the lamps by clicking on regions. In this talk, we show that we can complete the game for any knot projection with any state of lamps by considering "region crossing change" which is a local move on knot diagrams. This game is a joint work with Akio Kawauchi and Kengo Kishimoto.

Play Region Select!
Get Region Select for your android!

Panel Discussion

Topic: Qualifying Exams

Speaker: Maggy Tomova, The University of Iowa

Title: The salesman with marital problems and other questions about graphs

Abstract:

The traveling salesman problem is an old question that has been studied by mathematicians for almost a century. The question can be formulated as follows: Given a number of cities and the time to get from one city to another, what is the fastest route for a salesman to take so he visits all cities?

In this talk we will consider the exact opposite of this problem. Suppose the salesman wants to stay on the road for as long as possible. What is the best way to achieve this goal? We will show how to model this problem with graphs and solve it for certain families of graphs.

CCUT and coffee

Lead by: Kim McShane-DeBacco

Join us for coffee at Nicolletti's and a discussion about CCUT, College Certificate in Undergraduate Teaching. Kim McShane-DeBacco will lead the discussion. She is an Instructional Consultant here at UCSB. CCUT is an great program that UCSB offers to help prepare graduate students to teach at the undergraduate level.

Speaker: Claire Levaillant, UCSB

Title: An introduction to Claire's Ph.D. thesis and its generalizations.

Abstract: I will define the Birman-Murakami-Wenzl algebra abbreviated "BMW algebra", both in terms of algebraic relations and in terms of diagrams. I will show to you how I build a representation of the BMW algebra of type $A_{n-1}$ which is also a representation of the braid group on $n$ strands. The BMW algebra is based on two parameters. I will explain how I find complex values of the parameters for which the algebra is not semisimple. These values depend on $n$, where $n-1$ is the number of generators of the BMW algebra of type $A_{n-1}$ and also the number of generators of the braid group on n strands. I will then tell how I generalize this work to Coxeter type $D_n$. My talk at the topology seminar will be about type $E_6$ and you should then be finely prepared to understand it.

Speaker: Adriana Salerno, Bates College

Title: Rational Points and Hypergeometric Functions

Abstract: Hypergeometric functions seem to be ubiquitous in mathematics, particularly when counting rational points over finite fields. In this talk, we will show that the number of points over a finite field Fq on a certain family of varieties is a linear combination of hypergeometric functions. We will also give a brief introduction to working with p-adic numbers and use results by Koblitz and Gross to find explicit relationships. Finally, we will explain how these formulas could be useful for computing Zeta functions in the future and in extending some classical results in number theory.

Speaker: Abigail Thompson , UC Davis

Title: Knot complicated

Abstract: I'll talk about various methods of measuring how "complicated" a knot (like a knotted loop of string) is, and how much is known about each measurement for a few standard knots. I'll also talk about physical methods of sorting out knots, such as by gel electrophoresis. Finally I'll describe some preliminary results from a research project completed with a group of undergraduates at UCD, in which we found a good macro-scale method that seems to sort knots (made out of spaghetti)(seriously) in a manner similar to gel electrophoresis for knotted strands of DNA.

Informal Meet and Greet with Undergraduates

Speaker: Brittany Erickson, Stanford

Title: Introduction to mathematical models of earthquakes and an application to the interseismic period

Abstract: With the goal in mind of modeling earthquake rupture, we will start by establishing a model of how the solid earth responds to an applied force. Momentum balance with Hooke's law for the stress-strain relationship yields the elastodynamic wave equation. Plane wave solutions result in an eigenvalue problem with three eigenvectors corresponding to one longitudinal p-wave and two shear waves. We will then look at a 2-d example of the wave equation known as the anti-plane problem where a fault lies on the boundary of the elastic medium. The seismogenic zone along the fault is governed by a friction law, and the system is loaded by imposing steady creep on the down-dip extension of the fault. At the surface of the earth, the corners of the domain can potentially have incompatible boundary conditions which can be problematic computationally. Summation-by-Parts finite difference operators have many desirable properties including weak enforcement of boundary conditions through the Simultaneous Approximation Term. As a simple illustration we will consider this method applied to the one-way wave equation. Finally, my postdoctoral work has been the development of a time-stepping algorithm to account for quasi-static evolution in the interseismic period prior to an earthquake. We will discuss this idea in the anti-plane problem context to show how cycles of earthquakes can be simulated with corresponding slip velocities ranging over 10 orders of magnitude.

Panel Discussion

Topic: Advancing to Candidacy and Beginning Research

Speaker: Yeonhee Jang, Hiroshima University

Title : Introduction to bridge presentations of links

Abstract : This will be an introductory talk on my research, mainly on bridge presentations of links. We recall the definition and basic properties of bridge presentations of link, and I will introduce briefly studies on bridge presentations of links so far.

Organizational Meeting

Speaker: Elizabeth Thoren, UCSB

Title: Stability of Vortex Patches

Abstract: I'll introduce vortex patch solutions to Euler's equation for incompressible fluids (think hurricanes). Then we'll discuss how the conservation of certain quantities in Eulerian fluid flow leads to a nice stability result for circular patches.

Panel Discussion

Topic: How to do research

This week, we will be discussing the process of doing research. We will have on the panel distinguished researchers to share with us their experiences. Please join us and bring questions and/or comments!

Speaker: Chris Soteros, University of Saskatchewan

Title: Lattice Models of Polymer Entanglements

Abstract:

Self-avoiding polygon models have been used to study ring polymers (long closed chain molecules) in dilute solution for over 50 years. For such models, a vertex of the polygon represents a monomer unit and an edge of the polygon joins two monomer units which are chemically bonded together in the polymer. Distinct self-avoiding polygons on a lattice, such as the simple cubic lattice, are used to represent distinct conformations of a ring polymer. At equilibrium in dilute solution, each equal-length polygon is considered to be equally likely as a polymer conformation, and one is interested in the average spatial properties of the polymer as a function of its length. For example, there is much interest in their entanglement complexity (e.g. probability of being knotted), especially with respect to modelling enzyme action on circular DNA.

In this talk, I will review why polymer entanglements are of interest; then introduce the self-avoiding polygon model for ring polymers described above; and finally give an overview of some of the theoretical and numerical approaches for studying polymer entanglements with this model.

Short Talks

Speakers: Yen Duong and Teddy Einstein

Teddy's Title: Conjugacy Tests in the Nottingham Group

Abstract: Let K be a field of characteristic p. We study conjugacy of elements of the Nottingham group over K, $N(K) = t+t^2 K[[t]]$, a group of formal power series under composition. We will give a brief overview of the basic properties of the Nottingham group and some of the tools used to work with the Nottingham group. We use these tools to exhibit a test for conjugacy of torsion elements with order p developed by Benjamin Klopsch. Finally, we will present an original result generalizing the conjugacy test to elements which have a common p-th iterate.

Yen's Title: Signed minor-minimal intrinsically linked graphs in RP^3

Abstract: Graph theory, knot theory, and combinatorics combine in a talk in which we classify graphs that contain two linked cycles regardless of their embedding in RP^3.  First we explore what intrinsic linking means, then we find graphs with this quality, and finally we prove that we've found all of them.  This presentation is from my REU at SUNY Potsdam in 2009 and is very accessible.

Speaker: Kim Ruane, Tufts

Title: Geometric Methods in Group Theory

Abstract: In this talk we will see how to prove two standard facts from group theory using geometric methods. The first is about the symmetric group - a group most students come in contact with in an undergraduate abstract algebra course. We will prove the standard fact that each permutation can be assigned a label of "odd" or "even" in a well-defined way using the structure of a Cayley graph for this group. The second is about finitely generated free groups. We will prove that any nontrivial finitely generated normal subgroup of such a group is finite index. Again we will use the geometry of a Cayley graph to do the proof.

Speaker: Ani Dzhidaryan, UCSB

Title: Experts' Representational Knowledge of Division of Fractions

Abstract: The topic of fractions, and more specifically the division of fractions, remains to be one of the more challenging topics that both students and teachers grapple with. Recently, studies have suggested that the number line may serve as a representational tool that can help foster better understanding of this topic. Yet, in a complimentary study, we have found that teachers struggle with constructing a number line to represent division of fractions and would initially attempt to use an area model. In this exploratory study, we examined whether graduate students and professors within the math and physics departments would spontaneously see and use a number line when asked to visually represent division of fractions. Our results seem to suggest an initial preference for the area model, but our informants possessed the ability to construct a number line model when prompted to do so. Cross-national comparisons of teachers' and experts' representational preferences may further clarify whether the preference for the area model arises as an artifact of cultural practices (e.g., teaching practices) or is indicative of a more easily retrieved cognitive model.

Speaker: Joan Licata, Stanford

Title: An Introduction to Contact Geometry

Abstract: Contact geometry studies odd-dimensional manifolds equipped with some extra geometric structure. An active area of research, this field has connections to low-dimensional topology, Hamiltonian mechanics, and parallel parking. In this talk, I'll introduce some definitions and interesting examples, focusing particularly on the knot theory associated to contact three-manifolds.

Short Talks

Speakers: Ben Cote and Megan Maguire

Megan's Title: Solving Polynomials for Profit
Abstract: I will talk about the XL family of algorithms that attempt to break block ciphers (such as DES, and SAES) by modeling these ciphers as a system of multivariate polynomials. I will define mutant polynomials, and talk about how exploiting them might or might not lead to an improvement of the XL algorithm.

Ben's Title: Zero-divisor graphs, cut-sets, and maximal ideals.
Abstract: A zero-divisor graph is a graph whose vertices are all the nonzero zero-divisors of a finite commutative ring R. Two vertices a and b are connected by an edge if and only if ab=0. C. Ewing, M. Huhn, C. M. Plaut, D. Weber and I examined minimal sets of vertices which, when removed from a zero-divisor graph, separate the graph into disconnected subgraphs. We classified these sets for the zero-divisor graphs of all finite commutative rings with identity. I will be presenting a few standard results about zero-divisor graphs along with our results.

Time change: 2PM in South Hall 6635.

Speaker: Bill Jacob, UCSB

Title: The Development of Mathematical Knowledge for Teaching in Preservice Teachers: A Comparative Study

Abstract: The purpose of this presentation is to present results from of a design research study that explored the development of early "mathematical knowledge for teaching" (MKT) in undergraduates. Prospective elementary and secondary teachers participated in this study while enrolled in mathematics courses that blend mathematical content with the examination of the mathematical development of learners as evidenced in case studies. Part of the presentation will introduce the tools used in qualitative research in mathematics education and the second part will describe the research, which deals with the collegiate mathematics preparation of future K-12 teachers. This research is joint with Sarah Hough, Kyunghee Moon, and Monica Mendoza.

Speaker: Maria-Rita RD'Orsogna, California State University Northridge

Title: Viral entry into cells

Abstract: Successful viral infection of a healthy cell requires complex host-pathogen interactions. In this talk we focus on the dynamics specific to the HIV virus entering a eucaryotic cell. We model viral entry as a stochastic engagement of diffusing receptors and coreceptors on the cell surface. We also consider the transport of virus material to the cell nucleus by coupling microtubular motion to the concurrent biochemical transformations that render the viral material competent for nuclear entry. We discuss both mathematical and biological consequences of our model, such as the formulation of an effective integrodifferential boundary condition embodying a memory kernel and optimal timing in maximizing viral probabilities.

Panel Discussion

Topic: How to find an advisor

This week, we will be discussing the process of finding an advisor. Please join us and bring questions and/or comments!

Special Colloquium with the Algebra Seminar

Speaker: Kelli Talaska, Berkeley

Part 1: Planar networks, determinants, and generalizations Classical work provides an elegant relationship between determinants and path counting in acyclic directed graphs. This approach led to a complete combinatorial description of totally positive matrices. We will look at this elementary construction and explore several ways to extend beyond the class of totally positive matrices.

Part 2: A combinatorial description of the totally nonnegative Grassmannian The totally nonnegative Grassmannian is the subset of the Grassmannian in which all Plucker coordinates have the same sign. As with totally positive matrices, it is possible to provide a parametrization using certain weighted planar graphs. We will give combinatorial formulas (in both directions) for a bijection between points in the TNN Grassmannian and these special graphs.

Panel Discussion

Topic: How to pass the quals

This week, we will be discussing quals. Please join us and bring questions and/or comments!

Time and place: 2PM in the Quiet Room South Hall 4607A.

Panel Discussion

Topic: Technology in the Classroom

http://www.math.ucsb.edu/~lzirbel/ At 3h30 in SH6635, there will be a panel discussion on use of technology in the classroom and as a teaching tool. Daryl Cooper, Julia Galstad, Rahul Shah, and Laura Zirbel will be giving 5-10 minute introductions to their pet technologies followed by a Q&A session. Fuz Rogers will also be present on the panel to answer technical questions.
Daryl Cooper will be speaking about his innovative use of i>clickers in Math 34A. This simple tool has a wider range of use in the classroom than most people realize. There will be i>clickers for you to try.

Julia Galstad will demonstrate a few free online math apps that can make teaching more fun for instructors and students.

Rahul Shah will be speaking about our Graduate Resource Sharing site on Gaucho space that he set up with Sonja Mitchell last year. This is a file share on Gaucho Space where graduate students can load up anything that might help their fellow graduate students: old quizzes for teaching, worksheets, study guides, and also qualifying exam solutions.

Laura Zirbel will speaking about Gaucho Space- how to set up a course page, utilize all of the features, and why it is so great and worth the initial investment to figure it out.

Bring your laptops if you want to play along.

Speaker: Tara Davis, Vanderbilt University

Title: An Introduction to Geometric Group Theory

First Talk Abstract: As graduate students, we often hear about our professors research interests: algebraic number theory, representation theory, geometric group theory, etc. However, at least at the beginning of our careers, we have little idea of what doing research in these areas would actually entail. This talk will serve as an overview and introduction to the area of geometric group theory. We will explain how to view a finitely generated group as a geometric object. We will also introduce some of the specific topics of interest in this field.

Second Talk Abstract: We study the effects of subgroup distortion in the wreath products A wr Z, where A is finitely generated abelian. We show that every finitely generated subgroup of A wr Z has distortion function bounded above by some polynomial. Moreover, for A infinite, and for any polynomial, there is a 2-generated subgroup of A wr Z having distortion function equivalent to the given polynomial. If A is finite, then every finitely generated subgroup in A wr Z is undistorted.

Panel Discussion

Topic: Discussion on the Two-Body Problem

Come and listen to established professors discuss their experience finding jobs in academia together with their partners. We will have our very own Jon McCammond of the UCSB math department and his partner Mary Bucholtz of the linguistics department. We will also have Rena Levitt, who is currently a Visiting Assistant Professor at Claremont McKenna College. She (and her husband John) graduated from the UCSB Math department in 2008. This panel discussion is organized by Sonja Mitchell (fourth year graduate student).

Speaker: Ami Radunskya, Pomona College

Title: Mathematical approaches to modeling cancer treatments.

Abstract: What can mathematics tell us about the treatment of cancer? In this talk I will present some of work that I have done in the modeling of tumor growth and treatment over the last ten years. Cancer is a myriad of individual diseases, with the common feature that an individual's own cells have become malignant. Thus, the treatment of cancer poses great challenges, since an attack must be mounted against cells that are nearly identical to normal cells. Mathematical models that describe tumor growth in tissue, the immune response, and the administration of different therapies can suggest treatment strategies that optimize treatment efficacy and minimize negative side-effects. However, the inherent complexity of the immune system and the spatial heterogeneity of human tissue gives rise to mathematical models that pose unique analytical and numerical challenges. In this talk I will briefly discuss two mathematical problems that we have encountered in our work: optimization of systems of delay differential equations, and the analysis of spatial models that incorporate different time scales. No knowledge of biology will be assumed.

3rd Annual Women in Mathematics Symposium at Pomona College

Hypatian Seminar is funding 14 women from UCSB to go to the 3rd Annual Women in Mathematics Symposium at Pomona College including 9 talks. Take a look at the abstracts.

Film

Agora

Agora is a 2009 movie about Hypatia of Alexandria, our patron mathematician. It is set in 4th century Roman Egypt and is classified as historical fiction. Here is a review by the Los Angeles Times.

No seminar this week.
Instead please attend the following:

WEDNESDAY 3:30-4:30 in South Hall 6635 Amanda Beeson UCSD Recently graduated from UCSD, Dr. Beeson is a candidate for a position here at UCSB. Her research is on "Maximal Almost Abelian Extensions".

THURSDAY 3:30-4:30 PM South Hall 6635 Lillian Pierce Institute for Advanced Study at Princeton Originally from California, she recently earned her doctorate from Princeton this last year studying "Discrete Analogs in Harmonic Analysis".

Laura Zirbel, UCSB

Title: Mathematical Anecdotes and Jokes

Historical anecdotes and jokes can make any subject material engaging and dynamic. Mathematics has an exceptionally bizarre cast of characters including the insane, gamblers, blind geniuses and cults. The first part of this talk will be a Jeopardy style competition, followed by an informal exchange of our favorite material for undergraduate classes, as well as those stories we'll find any excuse to tell.

Linda Petzold, UCSB

Title: Discrete Stochastic Simulation of Spatially Inhomogeneous Biochemical Systems

Abstract: In microscopic systems formed by living cells, the small numbers of some reactant molecules can result in dynamical behavior that is discrete and stochastic rather than continuous and deterministic. An analysis tool that respects these dynamical characteristics is the stochastic simulation algorithm (SSA), which applies to well-stirred chemically reacting systems. However, cells are hardly homogeneous! Spatio-temporal gradients and patterns play an important role in many biochemical processes. In this lecture we report on recent progress in the development of methods for spatial stochastic and multiscale simulation, and outline some of the many interesting complications that arise in the modeling and simulation of spatially inhomogeneous biochemical systems.

Location change: South Hall 5607F (The PSTAT department)

Speaker: Ilesanmi Adeboye

Title: Hyperbolic Surfaces: An introduction.

Abstract: Orientable 2-dimensional manifolds are rich in mathematical structure. They connect complex analysis with geometry and group theory. A large subcategory of orientable 2-manifolds consists of those that admit a Riemannian metric with constant curvature -1; i.e., hyperbolic surfaces. The first half of the talk will cover the basic geometry of 2-dimensional hyperbolic space viewed as a subset of the complex plane. In the second half, we will explore the correspondence between hyperbolic surfaces and discrete groups of hyperbolic isometries. This is the first in a series of talks. The second talk will take place in the Discrete Geometry Seminar on January 27.

Speaker: Birge Huisgen-Zimmermann, UCSB

Title: The homology of finite dimensional algebras

Abstract: We will start with examples of finite dimensional algebras, placing special emphasis on path algebras of quivers (= finite directed graphs) modulo relations. Then we will introduce projective dimensions of modules over such algebras, again illustrated by examples. In particular, we will encounter a graphical method for computing projective dimensions in certain examples encountered earlier.

Speaker: Birge Huisgen-Zimmermann, UCSB

Title: The homology of finite dimensional algebras, part II

A continuation from the talk last week.

Monica Gabriela Cojocaru, visiting professor at UCSB

Title: OBJECTIVE AND SUBJECTIVE DECISION FACTORS: MODELLING CONSUMER BEHAVIOR FROM INDIVIDUAL TO POPULATION SCALE

Abstract: Modelling human decision processes and their impact on everyday life is today at the forefront of applied and social sciences. The need to understand, quantify and forecast how individuals and/or populations behave with respect to their surroundings has never been greater, in particular in the face of growing environmental challenges.

The process of decision making at the individual level has been studied extensively in operations research and management sciences, optimization, game theory, economics etc. The traditional approach is concerned primarily with the study of appropriately defined static (equilibrium) states and their properties, assuming that individuals make rational decisions. For constantly evolving systems however, this is an important, yet not sufficient, approach to describe societal behavior. This is a particularly important question if one studies innovation (new products) and science (new information about a product e.g. health benefits) driven problems, their complex relationship with policy making, and the ever changing population composition. In such a setting, the factors influencing individual and/or population attitudes are evolving, so the static theory cannot apply.

My research in this area is centered around several dynamic modelling approaches to population behaviour incorporating both objective and subjective decision factors. In this talk I concentrate on two time-dependent extensions of a standard, static model of consumer choice for differentiated products. We use both an agent-based and a PDE computational approach, and we incorporate social network effects. In this setting, an individual's choice depends not only on its characteristics (personality traits, perceived health benefits of a product, price of product, personal income), but also on the consumption choices of others in its social network. Of central interest is how consumers react to the introduction of a new product in the market. We are able to simulate socio-economic decision making criteria, under time-dependent individual and product characteristics, and to compute the adoption level of the new product in the population.

Time and location change: 3PM in South Hall 4607.

Speaker: Talithia Williams, Harvey Mudd

Title: Calculating target Cataract Surgical Rates for Africa

Abstract: Cataract remains the leading cause of blindness in Africa and planning for its treatment is a priority of the World Health Organization's VISION 2020 initiative. The cataract surgical rate (CSR), the number of operations done per million population, is a convenient indicator for planning and monitoring. However, estimating what the CSR needs to be to eliminate blindness requires one to take into account a number of factors and assumptions.

The recently developed Rapid Assessment of Avoidable Blindness (RAAB) survey uses a population-proportional-to-size sampling technique to select a representative group of people over 50 years old to receive a standard eye exam. We use current data from RAAB surveys in Africa to model the epidemiology of visually significant cataract and to estimate the incidence of cataract causing loss of visual acuity at different age levels. In this talk, I describe our method of estimating incidence from prevalence and how this information can be used to help set target CSR's for various geographical locations in Africa, taking into account important differences among populations.

In accordance with the theme of the Hypation Seminar, this talk will conclude with a discussion of the importance of mentoring women and underrepresented minorities in the mathematical sciences. I will share personal experiences and ways that individuals can aid in strengthening the ability of women and minority students to successfully complete graduate programs in the mathematical sciences.

Special Colloquium

Speaker: Idun Reiten, Norwegian University of Science and Technology

Title: From Bernstein-Gelfand-Ponomarev reflections to categorification of cluster algebras

Abstract: Around 1970 Bernstein-Gelfand-Ponomarev introduced reflection functors between representations of quivers with the same underlying graphs, but with different orientations. They used these functors to give a new interesting proof of Gabriel's classification theorem of the quivers of finite representation type in terms of Dynkin diagrams. We discuss the influence of this work on the recent theory of cluster categories, which were introduced in order to categorify a class of the cluster algebras introduced by Fomin-Zelevinsky. We also talk about some further developments.

This week we will be combining the Hypatian and Algebra Seminars, and calling the whole thing a "Special Colloquium" that will go from 3:30-5:00 with a 10 minute break for refreshments at 3:50PM. Prior to the break, the talk will be introductory, and afterwards it will be at the level of a typical Algebra Seminar.

Speaker: Carol Fan, Rand Corporation

Title: Setting Inventory Levels for Critical Items with Unpredictable Demands

Abstract: Inventory levels help warehouse managers determine when to order replenishments and what amount to order. Setting inventory levels for items with demands that can be predicted by a parametric equation, e.g., standard probability distribution, is relatively simple, but what can one do when demands are "unpredictable," meaning the cannot be modeled by a parametric equation? We look at the problem of setting inventory levels for items that are difficult to predict yet critical.

Talk is via sykpe.

Organizational Meeting

The Hypatian Seminar organizational meeting will be held at 3:30 in South Hall 6635. We will be discussing ideas for the fall and winter quarters. Everyone is welcome--bring ideas!

Agenda:

1. Current amount of money available
2. NSF Grant progess Report
3. Filling in remaining slots in the Seminar
4. Outreach -- possible workshop with Girls Inc
5. Involving undergrads

Panel Discussion

Topic: : How to get a job/post-doc

Confirmed panelists: Emille Davie, Ilsenami Adeboye, Elizabeth Thoren. Bring questions!

Speaker: Marion Moore, UC Davis

Title: High Distance Heegaard Splittings

Abstract: Any 3-dimensional manifold can be decomposed into two simple pieces: a Heegaard splitting. A Heegaard splitting can be regarded as a pair of subcomplexes in the complex of curves of the Heegaard surface. It is possible to relate geometric and combinatorial properties of these subcomplexes with topological properties of the manifold and/or the associated splitting. One such property is the Hemple distance of a Heegaard splitting. I will define the Hemple distance and give examples of desirable characteristics of high distance splittings.

Speaker: Rena Levitt, Pomona

Title: Combinatorial Geodesics in Simplicial Complexes

Abstract: In his 1912 paper, Max Dehn posed three seminal problems in combinatorial group theory: the word problem, the conjugacy problem, and the isomorphism problem. While stated in terms of finitely presented groups, each problem arose naturally in Dehn's study of fundamental groups of $2$-dimensional surfaces. In this talk, I will discuss one method to solve the word problem by constructing a geometric space the group acts on, the Cayley Graph. Then I will discuss using metric conditions to show that groups acting on CAT(0) simplicial complexes are biautomatic, a condition that gives a positive solution to both the word problem and the conjugacy problem for these groups. This relies on looking at the structure of combinatorial geodesics in the spaces.

Speaker: Cindy Wyels, CSUCI

Title: Achievable pebbling numbers

Abstract: Graph pebbling arose in a search for a "natural" proof of a number-theoretic conjecture of Erdös and Lemke, and has since taken on a life of its own. Begin with a distribution of pebbles on the vertices of a graph G. A pebbling move consists of taking two pebbles from a vertex and moving one to any adjacent vertex (while discarding the second). We say the distribution is solvable if at least one pebble may be placed on any target vertex, via a sequence of pebbling moves (possibly of length 0). The pebbling number of G is the smallest integer for which every distribution with that many pebbles is solvable. The pebbling number of a graph of order n must lie between n and 2n-1. We ask which integers may be realized as the pebbling number of a graph of order n. We specify sufficient conditions for an integer to be realized as a pebbling number, identify where certain gaps among potential pebbling numbers must occur, and obtain improved upper bounds for pebbling numbers.

Speaker: Alissa Crans, LMU

Title: Higher-Dimensional Algebra: Weakening the notion of Equality

Abstract: A fundamental problem in mathematics consists of determining whether two given mathematical structures are 'the same'. For example, knot theorists are interested in knowing when knots are the same, while algebraists like to know when groups are the same. But what exactly do mathematicians mean when they say that two gadgets are the same? Often, they mean "sufficiently the same for our purposes," and that purpose naturally differs from field to field. Higher-dimensional algebra, which enables us to refine our notion of 'sameness', is the study of generalizations of algebraic concepts obtained by developing category-theoretic analogs of set-theoretic concepts. We will see how higher-dimensional algebra can be used to explore mathematical interpretations of being 'the same' by carefully examining the concept of equality and comparing it to weaker notions of sameness.

Short Talks

Speakers: Cynthia Flores and Arielle Leitner

Cynthia's Title: Manifolds with Nonnegative Ricci curvature
Abstract: I will present some interactions among the various concepts of curvature and the relatively new concept of isotropic curvature. I will show some of the known results about Betti numbers pertaining to certain compact manifolds of nonnegative isotropic curvature and generalize them for nonnegative isotropic Ricci curvature. The results are proved using the Weitzenbock Formula and Hodge Theory.

Arielle's Title: Factors Related to the Success of CSU Chico Students
Abstract: What is a better indicator of student success: High School GPA or SAT score? In this presentation, we will discuss the relation of High School GPA, SAT score, race, gender, parental education and other factors to student success; where success is measured in terms of graduating GPA and years to degree.

Speaker: Elizabeth Thoren, UCSB

Title: The Spectrum and Stability for PDEs

Abstract: The spectrum of a linear operator is a generalization of eigenvalues for a matrix. Just as with eigenvalues and their eigenvectors, the spectrum of an operator tells us how the operator stretches certain vectors. I'll start the talk with a gentle introduction to spectral theory for linear operators and then use spectral theory to define a good notion of linear stability for PDEs. This talk is for a general mathematical audience -- no familiarity with PDEs or functional analysis required.

Speaker: Mike Williams, UCSB

Title: Morse Theory on Surfaces

Abstract: Morse theory deals with the analysis of critical points of differentiable functions, as in the second derivative test from calculus. Some nice topological interpretations result from this theory. In this talk, I will give an introduction to Morse theory and a discussion of how this theory can be used to distinguish surfaces. Any student with knowledge of multivariable-calculus and linear algebra should be able to understand most of the talk.

Speaker: Alethea Barbaro, UCLA

Title: Agent-based modeling of complex systems, and how to claim your mathematical territory after your doctorate

Abstract: At UCSB, I modeled the spawning route of the Icelandic capelin using an off-lattice interacting particle model. Now as a postdoc at UCLA, I am expected to make an impact well beyond my doctoral work. As such, I have had to explore and claim new mathematical territory. In this talk, I would like to show you how a researcher might expand on her mathematics after her dissertation. I will use my own experiences and my own research as a case study. The aim is that you will walk away from this talk with a basic understanding of the mathematics involved in agent-based complex systems and a more complete idea of how one moves forward as a research mathematician.

Organizational Meeting

The Hypatian Seminar organizational meeting will be held at 3:30 in South Hall 6635. We will be discussing ideas for the fall and winter quarters. Everyone is welcome--bring ideas!

Speaker: Dominic Assimaki, Georgia Tech

Title: Understanding the effects of near-surface geology to earthquake motion via seismogram inversion

Abstract: Observations of seismic ground motion in the last decade have contributed towards the understanding of the effects of near-surface geologic formations to earthquake motion, and have allowed advancements to be made in the state-of-knowledge and modeling of sediment response in-situ. To that end, we present a seismic waveform inversion algorithm that allows estimation of the soil properties and response to earthquake shaking using downhole seismogram array recordings. The algorithm is based on a global optimization scheme complemented by a local least-square fit operator in series, which improves the computational efficiency of the former, while avoiding the pitfalls of using the latter for the optimization of multi-modal, discontinuous and non-differentiable functions. Also, the non-stationary seismic signal is decomposed in the wavelet domain, which allows for equal weighting of the information across all frequency bands. The algorithm is next employed for the estimation of dynamic soil properties at geotechnical arrays operated by a variety of agencies and organizations (SCEC, USGS, CSMIP, Caltrans) in the Los Angeles basin. We show that while the optimization scheme provides robust estimates of the stiffness profiles, the attenuation structures are strongly affected by scattering effects of seismic waves in the near-surface soil layers. We finally present a sensitivity analysis on the dependence of the inverted attenuation structure to the frequency content of seismic input data, and conclude that for strongly heterogeneous soil formations, inversion schemes should explicitly uncouple the material (energy absorption) and scattering (energy redistribution) attenuation mechanisms to properly approximate the physics of earthquake wave propagation in the near-surface.

Discussion Leader: Brie Finegold

Topic: Math and the Media

Description: I will be showing some video clips and articles from the popular media that discuss mathematics. You may even learn how to rescue yourself from the following situation:

Speaker: Audrey Doughty, Florida Atlantic University

Title: Using Auslander-Reiten Theory to understand a category of poset representations

Abstract: In this talk, we'll use a combinatorial algorithm commonly used in Auslander-Reiten theory, as well as some special short exact sequences to pin down isomorphism types of representations of a particular poset, P.

Short Talks

Speaker: Audra Kosh

Audra has been working with Vadim Ponomarenko (from San Diego State). For the second half of the seminar we can socialize, and I will bring cookies!

Speaker: Dr. Julie Bergner, UC Riverside

Title: An Introduction to Modern Homotopy Theory

Abstract: We'll look at some of the basic ideas of classical homotopy theory in topology, and then discuss how to translate those ideas into more general settings, often outside of topology.

Speaker: Dr. Maribel Bueno, UCSB

Title: On the maximum exponent of circulant primitive matrices with fixed number of nonzero entries in the generating vector.

Abstract: This talk explores an interesting problem in Combinatorial Matrix Theory and its equivalent statements in other areas of mathematics. A matrix is said to be circulant if every row but the first one is obtained by shifting the previous row cyclically one column to the right. The first row of A is called the generating vector. A matrix A is said to be primitive if there exists a positive integer k such that A^k is a positive matrix. The minimum such k is called the exponent of A. An open question is: What is the set of exponents attained by circulant primitive matrices? In this talk we will present a conjecture to this question and give an answer to the question: What is the maximum exponent attained by circulant primitive matrices whose generating vector has exactly r nonzero entries. This talk will be accessible to undergraduates.

Holiday

Speaker: Chung-min Lee, CSU Long Beach

Title: Intensity Sensors and the Phase Reconstruction Problem

Abstract: Phase information of a light wave plays an important role in many optical applications, such as image recovering, optical design and surface measurement. However, the phase function of a light wave cannot be measured directly. Many phase reconstruction techniques have been developed, and some common ones will be presented. I then will focus on the method of intensity sensors which utilize the relationship between the intensity and phase functions of a light wave. Some results obtained by applying the Transport of Intensity Equation and the Weighted Least Action Principle will be presented, and a few related problems will be discussed.

Speaker: 26th Allison Kolpas, UCSB post-doc and alum

Title: Modeling and Analysis of Collective Motion in Animal Groups

Abstract: Many organisms move collectively in self-organized groups such as schools of fish, flocks of birds, swarms of locusts, and herds of wildebeest. Groups are capable of exhibiting a variety of different collective motion states. For example, a school of fish may swarm about a food source, travel in a highly polarized group, or form a circular milling pattern to avoid sit-and-wait predators. Although switching is observed in nature, the mechanisms behind it are not well understood. In this talk, I will present two models for collective motion which exhibit bistability, where switching may be robustly achieved through noise or external input. The first model, a biologically motivated individual-based model for group formation, displays stochasticity-induced switching between two metastable states. For this model, I will describe a coarse-grained computational framework for model reduction and analysis. The approach involves identifying a single dynamically meaningful coarse observable whose dynamics are described by an effective Fokker-Planck equation. The analysis leads to the construction of an effective potential which is used to perform bifurcation analysis, relating how behavioral interactions among individuals translate into collective movement patterns. The second model, a continuous-time kinetic model for collective motion with coupled oscillator dynamics, is inspired by the engineering literature for groups of autonomous vehicles. For this model, we consider how to design interaction rules which simultaneously stabilize two collective motion states. Variational methods are used to determine an optimal input to the steering control of an agent to induce switching between states.

Short Talks: Dynamical Systems

Speakers: Brittany Erickson and Melissa Hendrata

Brittany and Melissa will give short and accessible introductions to their research. Brittany studies applications to geophysics with Bjorn Birnir, and Melissa studies applications to microbiology also with Bjorn. They will each talk for about 20 minutes with a few minutes for questions at the end of each talk.

Speaker: Thalia Jeffres

Title: Vertical Blow-Ups and Applications to Capillarity

Abstract: The equation that describes the surface of a liquid standing in a capillary tube or container is a prescribed mean curvature equation which shares many features with minimal surfaces. If the container has a corner, the key to understanding the solution to this equation is a very careful examination of the behavior of the unit normal on approach to the corner through various directions. A colleague, Kirk Lancaster, and I used a blow-up procedure to describe which limiting positions were attained. I will describe the problem and some of the techniques used to solve it. This problem is a variational problem, and I will also describe some general features of variational problems. This talk will be accessible to all graduate students.

Panel Discussion

Topic: How to find your Advisor

Note the special meeting time on Wednesday rather than Monday! We will have a panel to lead a discussion on finding an advisor. Bring questions!

Speaker: Anne Thomas, Cornell

Title: Polyhedral complexes and lattices

Abstract: The class of polyhedral complexes includes many structures, such as simplicial complexes, cubical complexes, and buildings, which are important in many parts of mathematics. We will introduce several beautiful examples, and describe how they can be used to study lattices in locally compact groups.

Speaker: Abbe Herzig, CUNY Ablany

Title: Pulling Weeds or Sowing Seeds: Women in Graduate Mathematics

Some background info about our speaker: Dr. Herzig's research concerns equity and social justice in mathematics and science education at all levels. She is at the beginning of a 6-year research program concerning women and students of color in the post-graduate mathematical sciences, and is also investigating the low numbers of students of color in undergraduate engineering. She has developed courses and programs to help diverse populations of young people discover the relevance of mathematics and science to their interests and realities. She worked for 12 years as a statistician, much of that time for Consumers Union, the publisher of Consumer Reports magazine. She has consulted for the United Nations, the Yale School of Medicine, Brookhaven National Laboratory, and the Legal Defense Fund of the NAACP.

Film

Title: Julia Robinson and Hilbert's Tenth Problem

We will watch this biographical documentary on the life of mathematician Julia Robinson. Robinson was the first woman elected to the mathematical section of the National Academy of Sciences, and the first woman to become president of the American Mathematical Society. This film tells the story of Robinson's work with Russian mathematicians during the cold war that led to a solution to Hilbert's Tenth Problem. For more information, visit zalafilms.

Speaker: Julie Rowlett, UCSB

Title: The Fundamental Gap Conjecture

Abstract: What is the "fundamental gap?" Why is it sufficiently interesting that Yau and m. van de Berg made a conjecture about it? In this talk, I'll speak about joint work with Z. Lu on the Fundamental Gap Conjecture. This is a problem in spectral geometry, so if you are unfamiliar with spectral geometry, here is your opportunity to learn about it! I will give some fun and elementary (think multivariable calculus!) examples and explain our new results. The proofs of these results are rooted in a few basic principles, so it should be accessible to all math grad students.

Speaker: Clara Aldana, University of Bonn

Title: Determinants of Laplacians

Abstract: In the talk I will first explain how to define regularized determinants of Laplacians on closed manifolds. Then I will define relative determinants of Laplacians on surfaces with cusps and asymptotically cusps ends. At the end I give some reasons why to study them.

Speaker: Pascale Garaud, UC Santa Cruz

Title: The Solar Enigma

Abstract: The solar interior can be observed using Helioseismology, a method developed in the early 1980s. Measurements of plasma flows deep within the Sun have paved the way towards a better understanding of surface magnetic activity, but have also raised a number of new puzzles, most of which remain to be cracked. I will present new research on the subject of the interior rotation profile, and show how applied mathematics can help understand observations by combining large-scale numerical simulations and analytical toy models.

Activity

Title: Fun Math

In honor of Halloween week, we will be having an informal "fun math" session. Everyone is welcome! We'll provide plenty of problems, but feel free to bring your own to share (nothing that requires graduate-level math, please!).

Speaker: Iona Mihalia, Cal Poly Pomona

Title: Groups, Tessellations and the Rediscovery of Escher’s Solid

Abstract: Some simple plane tessellations can be viewed through algebra lens as generated by groups of transformations acting on the plane. Adding one dimension to the game leads us to the surprising rediscovery of Escher’s Solid.

Short Talks: Topology

Speakers: Teresita Ramirez-Rosas and Brie Finegold

Tere and Brie will give short and accessible introductions to their research. Brie studies Geometric Group Theory with Daryl Cooper, and Tere studies Knot Theory with Ken Millet. They will each talk for about 20 minutes with a few minutes for questions at the end of each talk.

Speaker: Guofang Wei, UCSB

Title: Synthetic Curvature

Abstract: In Riemannian geometry we study the shapes and sizes of manifolds with a Riemannian metric. Curvature is some second derivative of the Reimannian metric which gives a quantitive measure of the shape. What's curvature for metric spaces (ones with no differential structure)? While curvature itself may not be defined, curvature (lower or upper) bounds can be defined using synthetic curvature (curvature without derivative). We will start with the curvature of curves and end with some recent development in synthetic curvature.

Panal Discussion

Topic: Surviving Quals

There will be a panel of knowledgeable qual passers / qual writers to answer your questions about the dreaded qualifying exams that we all have to take. Discussion will likely include what you should expect, expectations of the graders, what to study, how to study, etc. Bring questions!

Speaker: Monica Vazirani, UC Davis

Title: Cores for partitions and the symmetric group

Abstract: You cannot study the symmetric group without stumbling across partitions(or Young diagrams). Cores are special partitions that encode particular algebraic and representation-theoretic information about the symmetric group in characteristic p (for instance, the blocks). Cores also arise in the affine symmetric group, as well as in the affine Lie algebra $\widehat {\mathfrak sl}_n$. We will play with the combinatorics of cores and hint at why their role in all these settings is no mere coincidence.

Workshop Leader: Alethea Barbaro, UCSB

Topic: Introduction to Mathjobs and finding academic positions online!

Abstract:  In the Hypatian Seminar, I will lead an interactive
introduction on how to use Mathjobs, the website where $\mu$ a.e. academic
mathematicians find job listings and apply for jobs.  In the seminar, I will
be able to access my mathjobs account and show how to navigate the site,
both finding listings and actually applying for them.  Even if you are very
early in your grad school career, you should consider coming--seeing this
might take the teeth out of applying for jobs when you get there!
Feel free to bring questions about the application process!

Speaker: Cathy Weinberger, UCSB Economics Dept.

Title: Gender Differences at the Top of the "Ability" Distribution (or: Using Mathematical Modeling to Show why Larry Summers was Wrong)

Abstract:  Low representation in the extreme upper tail of the mathematics
test score distribution is often assumed to explain the small numbers of
women in engineering, mathematics, computer science and physical science
(EMS) college majors and careers. However, this study finds that fewer
than one-third of the college-educated white men in the EMS workforce had
SAT-Math scores above the threshold previously presumed in the vocational
psychology literature. The lower-scoring male EMS college graduates have
more than an empty credential; they enjoy the same earnings advantage,
relative to other college graduates with the same scores, as high scoring
EMS majors.  This study also finds that white women enter EMS fields at no
more than half the rate of men with the same mathematics test scores. 
Both the large gender gap and the low ability threshold for EMS entry are
robust to modeling mathematics test scores as a noisy measure of ability.

Speaker: Mary Bucholz and Elena Skapoulli, UCSB Linguistics

Title: "What do you call an eigensheep?": Formulaic jokes as knowledge displays among undergraduate math and science students

Abstract: For the past two years, we have been carrying out an NSF-sponsored study of social interaction among UCSB undergraduate science majors (including math, physics, and chemistry majors), with the goal of understanding how science-oriented interaction can help promote the retention of students, especially but not exclusively women, in these fields. In this informal talk, we'll present a brief orientation to the project and offer some of our initial findings on one area of our research that has emerged as particularly interesting: the role of science humor in students' displays of scientific knowledge. Interactional studies of scientific practice have focused extensively on what might be called "the serious side of science," such as the interpretation and representation of data. We argue that another key component of scientific cultural practice is the circulation of science-based humor, which helps scientists (and their students) position themselves as members of a scientific community. We show that science humor, like humor generally, operates in part as a ìshort intelligence testî (Sherzer 1985:219) that simultaneously allows the initiator to display specialized knowledge and demands that recipients offer a corresponding display of understanding. Among undergraduate students, such humor creates the opportunity to display a science-oriented identity by allowing even novices to lay claim to a degree of specialized expertise.

Speaker: Gwen Fisher, Cal Poly

Abstract: Beaded beads are clusters of beads woven together with thread (usually around one or more large holes).   Their groups of symmetries are classified by the three-dimensional finite point groups, i.e. the finite subgroups of the orthogonal group of degree three, O(3).  Every finite subgroup of O(3) can be realized as the group of symmetries of a beaded  bead.  I will describe general weaving techniques  to accomplish this feat, as well as examples of a beaded bead realizing many of the finite subgroup of O(3) or, in the case of the seven infinite classes of finite subgroups, at least one representative beaded  bead for each class.  Other mathematical applications of bead weaving will also be discussed including polyhedra, fractals, graph theory, surfaces, and knots.

Seminar is cancelled this week so we can all so see the film being presented by the PSTAT department about the life and Mathematics of Wolfgang Doeblin. Read flier at http://www.pstat.ucsb.edu/files/WolfgangDoeblin.pdf

Speaker: Erica Flapan

Title: TBA

Abstract:TBA

Speaker: TBA

Title: TBA

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Happy Memorial Day!

Speaker: Luminita Vese, UCLA

Title: TBA

Abstract: TBA

Speaker: Sanjai Gupta, Harvey Mudd

Effective Classroom Strategies

Abstract: When people ask me what it's like to be a teacher, I say it's like acting, but you're allowed to make mistakes. So how does one act in the classroom? In this talk you will experience things I do in the classroom and hear practical advice gathered from my own teaching experiences.

Speaker: Audrey Terras, UCSD

Title: A new kind of zeta function: When number theory meets graph theory

Abstract: The talk is an introduction to zeta functions of graphs by comparison with the zeta functions of number theory such as Riemann's zeta function. Basic properties will be discussed, including: the Ihara formula saying that the zeta function is the reciprocal of a polynomial. I will then explore graph analogs of the Riemann hypothesis, the prime number theorem and connections with expander graphs and quantum chaos. References include my joint papers with Harold Stark in Advances in Mathematics. There is also a book I am writing on my website: http://math.ucsd.edu/~aterras/newbook.pdf .

Speaker: Alexandra Pettet, Stanford

Title: Groups and Spines

Abstract: One of the best possible situations to be in when studying a group G is to have a nice topological space on which it acts. "Nice" may mean that the space is contractible and cocompact, with the structure of a simplicial complex and a free G-action. This situation can make it possible, for example, to study presentations or cohomology of G. Usually we have to make do with a G-space which is not quite so nice, but we can often get by almost as well. For example, although we may not start with a space which is cocompact, we may be able to describe a G-invariant deformation retract which is cocompact; this is what we call a spine. I will describe examples for some important groups, namely the outer automorphism group of a free group and the special linear group SL_n(Z). I will also explain a theorem showing that our spine for SL_n(Z) is minimal, in the sense that it contains no smaller invariant retract; this is joint work with Juan Souto.

Panel: Jeff Stopple, Alethea Barbaro, Ryan Blair, Melissa Flora, Rena Levitt, and Peterson Tretheway

Topic: Surviving the Qualifying Exams

Abstract: It's a rite of passage we all go through. This weeks seminar will be a discussion different strategies you can use to successfully tackle your quals.

Panel Discussion: Lead by Julie Rowlett, UCSB

Topic: Math Research

Organizer: Brittany Erickson

Organizational Meeting

Topic: The Hypatian Seminar organizational meeting will be held at 3:30 in South Hall 6635. We will be discussing ideas for the fall and winter quarters. Everyone is welcome--bring ideas! Hope to see you there. There will be snacks!

Organizer: Brie Finegold

Life as a Teaching Assistant

Topic: This week we will have an informal discussion of teaching and being a teaching assistant. This is an opportunity for both inexperienced and experienced TA's to talk about how the first week of classes went, what our expectations and concerns are for the quarter, and how to become better instructors.

Organizer: Brie Finegold

Film Clip Day

Topic:   Today we will be showing clips of mathematics in pop-culture (Remember the show Square One with Math Net? If not, it's because you're too young), and people talking about math/science in American culture (A woman computer scientist reading an essay about her life taken from the anthology "She's Such a Geek!"). I would also like to leave a little time at the end to talk about how we've seen math protrayed in the media, especially with relation to women, and what we like/don't like about it. As always, there will be snacks!

Organizer: Brie Finegold

An Invitation to Undergraduate Women

Topic: This coming Monday, we will be welcoming undergraduates in mathematics, especially women, to attend Hypatian Seminar. We will have an informal meeting where graduate students, post-docs, and faculty can talk to undergrads about what it's like to do research, how it was during their first few years of grad school, and what it's like to be a woman in academia. We hope also that undergrads will come share with us their questions and their impressions and opinions of academic life so far.

Abstract: This talk is an introduction to the mathematical theories of liquid crys- tals. Liquid crystal phases form when a material has a degree of positional or orientational ordering yet stays in a liquid state. We present the static and hydrodynamic theories of liquid crystals and consider the minimizers of the energies and solutions of the governing equations as a way to describe the influence of the temperature or applied fields.

Speaker: Julie Rowlett, UCSB

Abstract: There will be two parts. Part I will be a summary of the interesting mathematics of the 6th International Conference on Lie Theory and Geometry, as well as some discussion of the connections between these 3 areas of mathematics. Part II will be a mini-guide for conferences: how to get invited, what to do when you're there, and what to do afterwards. It will be a very participatory talk, lots of questions welcome, and especially towards the end of the second part, comments will be welcome also.

Abstract: We will have an organizational lunch to discuss the following topics:

• Mentoring for incoming students
• Potential speakers for next year
• Conferences graduate students want to attend
• Suggested topics for discussions/workshops
  

Abstract: In this talk, I will present a to-do list of *everything* that you will need to have done by graduation and highlight the things you can do in the summer before graduation to make your last year easier. I will also give some general guidlines, insights and suggestions to help ease your last year of graduate school... At the end of the talk, I will also give some ideas, insights, and suggestions for the post-doctoral years.

Link to the slides from Julie's talk

Abstract: The Hypatian Seminar will have an organizational meeting today at 3:30 in South Hall 6635. We will be discussing ideas of the winter and spring quarters. Everyone is welcome--bring ideas! Hope to see you there.

Abstract: Hypatia (370-415 AD) is considered to be the last mathematician of the ancient world. This talk will be about the times she lived in as well as her work and her legacy.

Abstract: In this talk I discuss the proof of the following theorem: if $K$ is a compact nonpositively curved triangle-square complex, then its fundamental group is biautomatic. A triangle-square complex is a piecewise Euclidean $2$-complex with each $2$-cell isometric to either an equilateral triangle or square of unit side length. This reproves an generalizes earlier results of Gersten and Short.

Abstract: Beamer is a free program which you can download off the internet to make slick presentations. It plays nicely with LaTex. This will be an introduction to making presentations in Beamer. We will create a talk together which will show what Beamer can do. Then we will post it here for you to access. Come and bring friends!

Link to the Beamer Talk (PDF file)

Link to all the files needed to create the Beamer talk

Abstract: I will talk about some of the interesting mathematics talks I went to in February. Also, I will say what the AAAS is and why more mathematicians should consider becoming members. Come hear a smattering about "stylometry," detecting fraud using mathematics, what math researchers say you should do to improve math ed., and why Toy Story II looked better than the first one.

Link to Brie's PowerPoint Presentation

Abstract: We will discuss the works of the woman who broke the gender barrier in mathematics. She was the first major woman mathematician in modern times and the first one to become a professor in mathematics. Her work was fundamental and classical in PDEs, but less well known is that her work on the Kovalevsky top lead to important developments in integrable systems and algebraic geometry in the latter half of twentieth century. She had many brilliant mathematical insights but perhaps the most enduring one was the sufficiency condition in the classical Jacobi's theorem on integrable systems.