Columbia Home
Michael Harris elected to the American Academy of Arts & Sciences

Please congratulate Professor Michael Harris, who was recently elected as a member of the American Academy of Arts & Sciences!

Professor Michael Harris joins a distinguished list of scholars and thinkers from a variety of fields and disciplines. As posted on the Academy’s website:

“The Academy membership encompasses over 4,600 Fellows and 600 Foreign Honorary Members and reflects the full range of disciplines and professions: mathematics, the physical and biological sciences, medicine, the social sciences and humanities, business, government, public affairs, and the arts. Among the Academy’s Fellows are more than 250 Nobel laureates and 60 Pulitzer Prize winners.”

For a complete list of the 2019 members, including Professor Michael Harris, please visit:
https://www.amacad.org/content/members/newFellows.aspx?s=c

Print this page
Anna Wienhard (Heidelberg University)

Title: (Higher) Teichmüller Spaces and Beyond

Abstract:

The Teichmüller space of a surface parametrizes (marked) conformal structures. It covers the moduli space of Riemann surfaces and carries many interesting structures in its own right. Higher Teichmüller spaces are generalizations of Teichmüller space in the context of Lie groups of higher rank such as SL(n,R).

They are related to Higgs bundles, bounded cohomology, dynamics, as well as cluster algebras or total positivity. The talk will provide an introduction to higher Teichmüller spaces and showcase some of the connections.

Wednesday, April 24, 4:30 – 5:30 p.m.

Mathematics 520
Tea will be served at 4:00 p.m.

Print this page
Spring 2019 Kolchin Lecture

Spring 2019 Kolchin Lecture

Come join us on Wednesday, April 3, 2019 between 4:30 – 5:30pm in Rm 520, Professor Lars Hesselholt (Nagoya University & University of Copenhagen) will be giving a special lecture titled Higher Algebra and Arithmetic.

ABSTRACT

The natural numbers record only the result of counting and not the process of counting. As algebra is rooted in the natural numbers, the higher algebra of Joyal and Lurie is rooted in a more basic notion of number which also records the process of counting. Long advocated by Waldhausen, the arithmetic of these more basic numbers should eliminate denominators. Notable manifestations of this vision include the Bökstedt-Hsiang-Madsen topological cyclic homology, which receives a denominator-free Chern character, and the related Bhatt-Morrow-Scholze integral p-adic Hodge theory, which makes it possible to exploit torsion cohomology classes in arithmetic geometry.

Moreover, for schemes smooth and proper over a finite field, the analogue of de Rham cohomology in this setting naturally gives rise to a cohomological interpretation of the Hasse-Weil zeta function by regularized determinants, as envisioned by Deninger.

Tea will be served at 4 pm in 508 Mathematics.

*Kolchin Lecture Flyer*

Time & Location

Wednesday, April 3, 2019 between 4:30 – 5:30 pm in Rm 520

Print this page
Columbia Summer Math Research Experience for Undergraduates

The Mathematics Department runs a 10 week summer research program, aimed at rising junior and senior undergraduate math majors. Students participating in the program work closely with faculty members and graduate students in a small group setting.

Accepting applications through Friday, March 8, 2019

May 28 – August 1, 2019

For more information please visit;

www.math.columbia.edu/reu

 

Print this page
Liouville Quantum Gravity As a Metric Space and a Scaling Limit

Special Seminar

Come join us Monday, February 11, 2019 at 4:30 pm in RM 507, Professor Jason Miller (University of Cambridge) will be giving a special lecture about “Liouville Quantum Gravity As a Metric Space and a Scaling Limit”.

Abstract

Over the past few decades, two natural random surface models have emerged within physics and mathematics. The first is Liouville quantum gravity, which has its roots in string theory and conformal field theory from the 1980s and 1990s. The second is the Brownian map, which has its roots in planar map combinatorics from the 1960s together with recent scaling limit results.  We will describe work with Sheffield in which it is shown that Liouville quantum gravity (LQG) with parameter $\gamma=\sqrt{8/3}$ is equivalent to the Brownian map and work with Gwynne which use the $\sqrt{8/3}$-LQG metric to prove the convergence of self-avoiding walks and percolation on random planar maps towards SLE(8/3) and SLE(6), respectively, on a Brownian surface.

Print this page
Cardy Embedding of Random Planar Maps

Special Seminar

Come join us Wednesday, February 6, 2019 at 4:30 pm in RM 507, Professor Nina Holden (ETH, Zürich) will be giving a special lecture about “Cardy Embedding of Random Planar Maps”.

Abstract

A random planar map is a canonical model for a discrete random surface which is studied in probability, combinatorics, mathematical physics, and geometry. Liouville quantum gravity is a canonical model for a random 2d Riemannian manifold with roots in the physics literature. In joint work with Xin Sun, we prove a strong relationship between these two natural models for random surfaces. Namely, we prove that the random planar map converges in the scaling limit to Liouville quantum gravity under a discrete conformal embedding which we call the Cardy embedding.

Print this page
On the Black Hole Stability Problem

Special Seminar

Come join us Monday, February 4, 2019 at 4:30 pm in RM 507, Professor Jérémie Szeftel (Université Pierre et Marie Curie) will be giving a special lecture about “On the Black Hole Stability Problem”.

Abstract

I will introduce the celebrated Kerr black hole stability problem, which asks whether metrics of the Kerr family are stable as solutions to the Einstein vacuum equations of general relativity. I will then focus on recent progress obtained in my joint work with Sergiu Klainerman.

Mathematics Hall, Room 507

Monday, February 4, 2019 at 4:30 pm

Print this page
Memorial Service for Michael Zhao

 

A memorial service for Michael Zhao will be held in Garden Room 2 of Faculty House on Saturday,  February 2 at 12 pm.  A reception will follow the service.  All are welcome.

Michael Zhao was a first-year doctoral student whose sudden and unexpected loss on December 8 was shattering for everyone in the Department.  He touched many of our lives during the short time he spent here and will be missed by all.

Print this page
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”.

Abstract

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

formula.

 

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”.

Abstract

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