Matthew Kahle

Samelson Postdoctoral Fellow
Stanford University
450 Serra Mall, Building 380-382X
Stanford, CA 94305-2125
email: mkahle at math dot stanford dot edu

Matt Kahle giving a talk

About

I came to Stanford as a postdoctoral fellow in the fall of 2007. My mentors here are Gunnar Carlsson and Persi Diaconis. I completed my Ph.D. in 2007 at the University of Washington, where my thesis advisors were Eric Babson and Chris Hoffman. I am also affiliated with Stanford's TMSCSCS group. Some expository mathematical writings can be found on my blog.

Potential employers are invited to view my cv, research statement, and teaching statement. Letters of recommendation are available from Eric Babson, Gunnar Carlsson, Persi Diaconis, Chris Hoffman, Yuval Peres, and Shmuel Weinberger (research), and Ravi Vakil (teaching).

Research

I am broadly interested in interactions of probability and statistical physics with topology, geometry, and combinatorics. Some of my work has applications to the emerging field of topological data analysis. My recent papers are available on the arXiv.

An Erdos-Renyi random clique complex on n=100 vertices. Betti numbers of a random Rips complex on n=100 vertices.

Teaching and seminars

In Spring 2010 I will teach Modern Algebra, Applied Field Theory, and Mathematics of the Rubik's Cube (webpages coming soon). In Fall 2009 I ran the Polya problem solving seminar and organized the William Lowell Putnam competition at Stanford. Together with Persi Diaconis, I organized a seminar on "graph homomorphisms". In Summer 2009, I taught MATH 53 (ODE's with linear algebra). In Spring 2009 I taught MATH 108 (Combinatorics) and MATH 161 (Set Theory).

Invited talks

Geometry seminar, U Toronto, March 8, 2010
Combinatorics seminar, Dartmouth, March 1, 2010
Colloquium, Cleveland State, February 26, 2010
Combinatorics seminar, UC Berkeley, February 22, 2010
Colloquium, U Oregon, January 25, 2010
Joint seminar in probability and topology, U Oregon, November 20, 2009
Probability seminar, Stanford, November 9, 2009
Applied topology, U Chicago, November 5, 2009
Topological complexity of random sets, American Institute of Mathematics, August 10-14, 2009
TMSCSCS seminar, Stanford, May 18, 2009
Data analysis using computational topology and geometric statistics, Banff, March 8-13, 2009
Probability seminar, U Washington, February 9, 2009
Discrete math seminar, UC Berkeley, February 4, 2009
Probability seminar, Duke, October 30, 2008
Computational algebraic topology, 0berwolfach, June 29-July 5, 2008
Topology seminar, U Oregon, April 22, 2008
Colloquium, Cal State East Bay, February 22, 2008
Bay Area Discrete Math Day, Google, October 20, 2007
Geometry/topology seminar, UC Davis, October 18, 2006
Probability seminar, UC Berkeley, October 11, 2006
MSRI program in computational applications of algebraic topology, Fall 2006.
Combinatorics seminar, U Washington, April 19, 2006

Papers and preprints

Random geometric complexes

(submitted, 2009)

An application of disc packing to statistical mechanics

(submitted, 2009)

Points in a triangle forcing small triangles

(Geombinatorics 18 (2009), no. 3, 114--128.)

The fundamental group of random 2-complexes

(w/ Eric Babson and Chris Hoffman, submitted to J. Amer. Math. Soc., 2008)

Topology of random clique complexes

(Discrete Math. 309 (2009), no. 6, 1658--1671.)

The neighborhood complex of a random graph

(J. Combin. Theory Ser. A 114 (2007), no. 2, 380--387.)

Scatters, unavoidable shapes, and crystallization

(Geombinatorics 15 (2006), no. 3, 138--149.)

A generalization of the chromatic number of the plane.

(Geombinatorics 10 (2000), no. 2, 69--74.)


In preparation

The chromatic number of random graphs on spheres
Warmth and mobility of random graphs (w/ Sukhada Fadnavis)
Non-monotone heierarchical clustering via Morse Theory (w/ Gunnar Carlsson and Jackson Gorham)

Travel

recent:
Probabilistic Techniques and Applications, IPAM-UCLA, Oct. 5-9
Duke, Oct. 21-23
U Chicago, Nov. 3-6
U Oregon, Nov. 17-18
AMS-MAA Joint Meetings, San Francisco, Jan. 13-16
U Oregon, Jan. 25

upcoming:
UC Berkeley, Feb. 22
Cleveland State, Feb. 25-26
Dartmouth, Mar. 1-3
U Toronto, Mar. 8-10
Case Western Reserve, Mar. 18-19
ICM, Hyderabad India, August?