Columbia Home
Super-Teichmüller Spaces, Spin Structures, Penner Coordinates, and Applications

Special Seminar

Come join us Friday, February 1, 2019 at 4:30 pm in RM 507, Professor Anton Zeitlin (Louisiana State University) will be giving a special lecture about “Super-Teichmüller Spaces, Spin Structures, Penner Coordinates, and Applications”.


The Teichmüller space, which parametrizes Riemann surfaces, is a

fundamental space that is important in many areas of mathematics and physics.

Recently, generalizations of this space have been intensely studied.  Examples of 

such higher Teichmüller spaces are the so-called super-Teichmüller

spaces. They appear in the application of the combinatorial approach to spin

structures on Riemann surfaces and generalizations to supermanifolds. The

super-Teichmüller spaces naturally  arise as higher Teichmüller spaces,

corresponding to supergroups that play an important role in geometric

topology, algebraic geometry, and mathematical physics.


In this talk, I will give a solution of the long-standing problem

of describing an analogue of Penner coordinates on super-Teichmüller

spaces and their generalizations. The importance of these coordinates is

justified by two remarkable properties: the action of the mapping class

group is rational and the Weil-Petersson form is given by a simple explicit



I will end my presentation with a description of some of the emerging

applications of this theory.

Mathematics Hall, Room 507

Friday, February 1, 2019 at 4:30 pm

Print this page
Principal Bundles and Diophantine Geometry

Special Seminar

Come join us Monday, January 28, 2019 at 4:30 pm in RM 507, Professor Minhyong Kim (University of Oxford) will be giving a special lecture about “Principal Bundles and Diophantine Geometry”.


Principal bundles and their moduli spaces have been important objects of study and essential tools in the geometry and topology of manifolds for at least the last fifty years. This talk will describe their applications to number theory, especially the theory of polynomial equations and their rational or integral solutions.

Mathematics Hall, Room 507

Monday, January 28, 2019 at 4:30 pm

Print this page
Graduate Topics Courses

The Graduate topics courses for Spring 2019 are now available through the following link:

Graduate Topics Courses




Print this page

Come join us on Wednesday, October 31, 2018 between 4:30 – 5:30pm in Rm 520 and Thursday, November 1, 2018 between 5:30 – 6:30pm in Rm 417, Professor Eugenia Malinnikova (Norwegian University of Science and Technology) will be giving a special lecture titled An improvement of Liouville’s theorem for discrete harmonic functions.

“The classical Liouville theorem says that if a harmonic function on the plane is bounded then it is a constant. At the same time for any angle on the plane, there exist non-constant harmonic functions that are bounded everywhere outside the angle. The situation is different for discrete harmonic functions on the standard square lattices. The following strong version of the Liouville theorem holds on the two-dimensional lattice. If a discrete harmonic function is bounded on 99% of the lattice then it is constant. Simple counter-example shows that in higher dimensions such improvement is no longer true.

We will present some discrete methods, compare the behavior of continuous and discrete harmonic functions and discuss some related questions and motivation.
The lectures are based on a joint work with L. Buhovsky, A. Logunov and M. Sodin.”

Tea will be served at 4 pm in 508 Mathematics.

*Joseph Fels Ritt Lecture Flyer*

Time & Location

Wednesday, October 31, 2018 between 4:30 – 5:30 pm in Rm 520


Thursday, November 1, 2018 between 5:30 – 6:30 pm in Rm 417

Print this page
Graduate Topics Courses

The Graduate topics courses for Fall 2018 are now available through the following link;

Graduate Topics Courses

Print this page

Come join us on Mondays at 1:10 pm in RM 507. Starting Monday, September 10, 2018Professor Walter Schachermayer (University of Vienna), will be giving a special lecture titled;

Asymptotic Theory of Transaction Costs

“One of the great features of traditional asset pricing theory is the assumption that there are no market frictions. In particular, one assumes that there is no bid-ask spread, so that no transaction costs have to be considered. This bold simplification of the real world situation was crucial to clarify the picture.

In a second step, however, it becomes important to carefully analyze the impact of transaction costs on the optimal behaviour of economic agents. Special emphasis will be given to asymptotic results, i.e., the limiting behaiviour when transaction costs tend to zero.

In the first half of the series of lectures we shall develop the basics of this theory and subsequently apply these results to a study of the classical Black-Scholes model.

In the second half we shall focus on applications which lead beyond the usual semi-martingale framework. A typical example will be a price process driven by fractional Brownian motion. This setting does not fit into the usual no arbitrage framework as these processes fail to be semi-martingales. The consideration of (small) proportional transaction costs allows us to find shadow price processes attached to these models, which allows to apply the well developed martingale theory also to these models.”

Time & Location

Mondays at 1:10 pm – 2:25 pm

Mathematics Hall, Room 507

*Minerva Lecture Flyer*

Print this page

Geometric aspects of p-adic Hodge theory


“Building up in a leisurely fashion, we will describe some recent advances in our understanding of the cohomology of algebraic varieties over p-adic fields, especially the integral cohomology. The main goal of the course is to define prismatic cohomology and explain how it unifies the various cohomology theories of interest in p-adic geometry. “

*Samuel Eilenberg Lecture Flyer*

Print this page
CONGRATULATIONS to Professor Dusa McDuff

2018 Sylvester Medal winner

Congratulations to Professor McDuff who was selected as the 2018 Sylvester Medal winner. The Sylvester Medal is now awarded annually for an outstanding researcher in the field of mathematics. McDuff will be awarded at the Royal Society’s Anniversary Day in November 2018 for leading the development of the new field of symplectic geometry and topology.

For more information please visit the link below;


Print this page
CONGRATULATIONS to Professor Corwin

2018 IMS Fellow

“Ivan Corwin, Professor of Mathematics, Columbia University, has been named Fellow of the Institute of Mathematical Statistics (IMS).  An induction ceremony will take place on July 2, 2018, at the IMS Annual Meeting in Vilnius, Lithuania.

Dr. Corwin received the award for groundbreaking contributions in integrable probability, especially the theory of Macdonald processes, stochastic quantum integrable systems, and their connections with stochastic partial differential equations, random growth models, interacting particle systems, and the Kardar-Parisi-Zhang universality.

Each Fellow nominee is assessed by a committee of his/her peers for the award.  In 2018, after reviewing 37 nominations, 20 were selected for Fellowship.  Created in 1935, the Institute of Mathematical Statistics is a member organization which fosters the development and dissemination of the theory and applications of statistics and probability. The IMS has 3,500 active members throughout the world.  Approximately 10% of the current IMS membership has earned the status of fellowship”.

Print this page
Math + Democracy

Join us for a series of talk on Tuesday May 8, 2018 at 12pm. This talk will be given by Professor Wesley Pegden (Carnegie Mellon University, Math department) held at NYU, Center for Data Science, 60 Fifth Ave, Room 150.


“Detecting Gerrymandering with Mathematical Rigor”


In February of this year, the Pennsylvania Supreme Court found Pennsylvania’s Congressional districting to be an unconstitutional partisan gerrymander.  In this talk, I will discuss one of the pieces of evidence which the court used to reach this conclusion.  In particular, I will discuss a theorem which allows us to use randomness to detect gerrymandering of Congressional districtings in a statistically rigorous way.

Print this page