John D. Mangual

I am a 3rd-year (out of 5 or 7) graduate student at UCSB in mathematical physics. I like problems in flat surfaces and large-N combinatorics, which are visually intuitive or deal with statistical algorithms or chaotic dynamical systems.

Instead of having a deep interest in one area, I have superficial interests in a variety of areas -- a sort of generalist attitude. And I am a curmudgeon. I complain combinatorics papers are too combinatorial, algebraic geometry papers are too algebraic, ergodic theory and determinantal processes papers are too analytic.

Here are problems that interest me these days:

• Combinatorial topology and relation to matrix models and the moduli space of curves via Wick's theorem
• The character theory of finite groups. Plethysms/schur functors of finite group representations. Invariant theory of finite groups.
• Veech surfaces and their relation to continued fractions.
• Generalizations of the Weyl-equidistribution theorem via nilmanifolds.
• The Robinson-Schensted algorithm and generalizations. Asymptotics.
• The Artic circle phenomenon, knutson-tao-puzzles, interacting particle systems and orthogonal polynomial ensembles.
• Free-fermions in combinatorics and algebraic geometry.
• Topological solitons and the Grassmanian.

These are pure math questions that borrow tools from (and hopefully contribute to) topics like 2D quantum gravity, 2D Yang-Mills, AdS/CFT correspondence, Holography, Integrable Systems, D-branes, AGT correspondence and BPS solitons in N=2 Supersymmetric Yang-Mills theory.

Current Classes [Winter]

Winter 2012

Attending the Novel Numerical Methods and Physics of Graphene workshops at KITP.

The material Graphene and the continuously varying families of Conformal Field theories (AdS/CFT correspondence) have gotten a lot of attention as a material last few years.

These two conferences, side by side, continue the link between high-energy and condensed matter physics emphasized last quarter.

• Phys 210A - Electricity & Magnetism w/ Mark Srednicki
• Phys 230A - String Theory w/ Joe Polchinski
• Math 240B - Seiberg-Witten Theory w/ Doug Moore

Fall 2011

Attending the Topological Insulators and Holography/Fermions/Renormalization workshops at KITP.

• Phys 205A - Classical Mechanics w/ David Berenstein

2010-2011

I spent Fall quarter as visiting graduate student at IPMU in Kashiwa, Japan, working with the Math and String Theory groups. However, I was enrolled in one class (QFT) at UCSB.

• Reading course on Baik-Deift-Johansson conjecture.
• Reading course on Wall-Crossing, Hitchin Systems and WKB Approximation.
• Auditing Math 229B on the Standard Model
• Math 221B Homotopy Theory
• Phys 221AB Quantum Field Theory
• Teaching Assistant for Math 5A/5AI (Differential Equations) with Elizabeth Thoren.
• Caltech/Tokyo U: Mathematical Techniques in String Theory w/ Hirosi Ooguri

2009-2010

• Math 240ABC: Differential Geometry
• Math 237AB: Algebraic Geometry
• Math 243ABC: Ordinary Differential Equations
• Phys 215ABC: Quantum Mechanics

Notes, Drafts

Mostly expository... can't find it anywhere on the net in a unified place.

How do Add Divegent Series

The Euler Characteristic of Random Branched Covers on the Torus

Go (Weiqi) Baduk:

I am director of the East Coast Go Camp. I spent last summer (2009) in Shantou, China studying Go with Feng Yun, one of three female 9-dan professionals in the world. My KGS and WBaduk name is mrcactu5 and I am 4K or 6K depending on the server.

Dots and Boxes / Hex

I am MonsieurCactus on Little Golem where you can find me playing Dots and Boxes, Hex, mini-Go and Twixt. Interested in Combinatorial Game Theory and surreal numbers.