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CONGRATULATIONS to Professor Birman; emeritus research professor, department of mathematics, Barnard College

Professor Joan Birman was elected as a new member of the National Academy of Sciences.

“The National Academy of Sciences is a private, nonprofit institution that was established under a congressional charter signed by President Abraham Lincoln in 1863. It recognizes achievement in science by election to membership, and—with the National Academy of Engineering and the National Academy of Medicine—provides science, engineering, and health policy advice to the federal government and other organizations.”

For the full announcement please visit;

2021 NAS Election (

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Incoming class of 2021

The incoming graduate class for 2021 has been announced. For a list of the new students, please visit the incoming class page.

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January 19: Junliang Shen

Title: The P=W conjecture and hyper-Kähler geometry.

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January 14: Elena Giorgi

Title: The stability of black holes with matter.

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January 12: Daniel Álvarez-Gavela

Title: K-theoretic Torsion Invariants in Symplectic and Contact Topology.

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Incoming class of 2020

The incoming graduate class for 2020 has been announced. For a list of the new students, please visit the incoming class page.

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On February 12, Samuel Eilenberg Professor of Mathematics Andrei Okounkov was elected to Foreign Membership in the Royal Swedish Academy of Sciences.  He joins a distinguished company of Foreign Members including Pierre Deligne and Jean-Pierre Serre.  Many congratulations to Andrei!

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Heat Equations in Analysis, Geometry, and Probability

“In its most basic form, the heat equation is a partial differential equation that describes the evolution of temperature in space over time. This and similar equations play a central role in diverse fields. The goal is to provide an introduction to the heat equation and its generalizations, including connections to geometry and geometric flows, probability, and, of course, analysis.”

*Samuel Eilenberg Lecture Flyer*

Tuesdays at 2:40 pm

Room 520, Mathematics Hall

2990 Broadway (117th Street)

First lecture: January 28, 2020

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Graduate Topics Courses in Spring 2020

The Department is offering 7 graduate topics courses in Spring 2020.  Titles and abstracts may be viewed here.

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The Fall 2019 Joseph Fels Ritt Lectures, by Professor Neshan Wickramasekera, will take place on Wednesday, October 23 and Thursday, October 24, 2019Professor Neshan Wickramasekera (Cambridge University) , will deliver a two talk series titled:

Lecture 1: Variational theory of minimal hypersurfaces of Riemannian manifolds

Lecture 2: Regularity of CMC and prescribed-mean-curvature hypersurfaces

A fundamental idea in the study of partial differential equations is to introduce generalized solutions and establish, possibly subject to further conditions, smoothness of the generalized solutions. Having in place such a “regularity theory” is useful in many ways: besides reducing the question of existence of classical (i.e. smooth) solutions to that of existence of generalized solutions,
it enables, in some instances, finding functions that are classical solutions away from a small set of non-smooth points—the best hope when everywhere smooth solutions do not exist. It also often facilitates study of weak limits of classical solutions. For much the same reasons as in PDE, it is of interest to study regularity of appropriately defined generalized submanifolds of a Riemannian manifold satisfying natural geomertic constraints related to their variationally defined mean curvature. Unlike in the PDE context however, a serious difficulty in this goemetric setting stems from a priori variable multiplicity of the generalized submanifolds; in fact in arbitrary codimesion, many regularity issues related to multiplicity remainpoorly understood.

These lectures will describe progress made in the past several years for a large class of hypersurfaces where it is shown that this multiplicity issue has a satisfactory answer. The work culminates in a sharp regularity and compactness theory subject to certain structural conditions on the hypersurfaces and appropriate control on their mean curvature, mass and the Morse index (with respect to the relevant functional). The work includes minimal (i.e. zero mean curvature) and constant mean curvature (CMC) hypersurfaces as important special cases. We will also discuss applications of the theory including a streamlined PDE theoretic alternative to the classical Almgren–Pitts min-max existence theory for minimal hypersurfaces.

The first lecture, intended for a general mathematical audience, will focus on the minimal hypersurface theory in fairly broad terms. The second lecture will discuss key differences for general mean curvature constraints (focusing on CMC) and some aspects of the proofs of the main theorems in all cases. The lectures will in part be based on a series of speaker’s works some of which are separate joint projects with C. Bellettini, O. Chodosh and Y. Tonegawa.

Lecture 1

Wednesday, October 23, 2019 in room 520 from 4:30 – 5:30pm

Lecture 2

Thursday, October 24, 2019 in room 417 from 5:30 – 6:30pm

Tea will be served at 4 pm in 508 Mathematics.
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