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Elena Giorgi awarded Sloan Fellowship

Congratulations to Elena Giorgi, an Assistant Professor in the Department of Mathematics, who was recently awarded a prestigious Sloan Fellowship!

Sloan Fellowship are awarded to “the most promising scientific researchers working today. Their achievements and potential place them among the next generation of scientific leaders in the U.S. and Canada..” For more information on the fellowship please visit:

The full list of 2024 recipients, including two other Columbia faculty, is available at, and an official press release from Columbia can be read here

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Spring 2024 Joseph Fels Ritt Lectures

Speaker: Blaine Lawson (Stony Brook)

2/15 – First Lecture: On compact minimal surfaces in S^3

Abstract: I will present a construction of compact minimal surfaces in the Euclidean three-sphere. In the orientable case, surfaces of every genus can be minimally embedded. In the non-orientable case, every surface but the real projective plane can be minimally immersed. For the projective plane, no such immersion exists.

These surfaces have some charm, and they also relate to the general topic of singularities of minimal three-folds in four dimensional spaces. This work was inspired many years ago by Professor Eugenio Calabi.

2/16 – Second Lecture: Nonlinear PDE’s and Potential Theories

  1. How does one deal with a partial differential equation when there is no natural operator?
  2. Given a differential operator, are there other operators with the same solutions but different useful properties? In fact can one radically change the operator to something tractable, in a way that enables solving the original equation?
  3. Does the space of subsolutions (or, equivalently, the space of supersolutions) give rise to a potential theory where interesting and relevant theorems can be proved?

These questions arose in my work with Reese Harvey. We discovered that while calibrated manifolds do not usually have analogues of the holomorphic functions that exist in the Kähler case, they do have analogues of plurisubharmonic functions. This started a long investigation. I will discuss various highlights of that work, and also some responses to these questions.

Thursday, February 15, 2024 @ 4:30 PM (407 MATH)

Friday, February 16 , 2024 @ 2:00 PM (312 MATH)


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Special Colloquium

Special Colloquium

Speaker: Toby Gee (Imperial College London)
Title: Modularity of genus 2 curves
Abstract: I will give an accessible introduction to some problems in the Langlands program. In particular, I will discuss work in progress with George Boxer, Frank Calegari, and Vincent Pilloni in which we prove the modularity of a positive proportion of curves of genus 2.

Date and Time: Tuesday, February 6, 4:30 PM
Location: 407 Mathematics

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Special Lecture Series Resumes

Special Lecture Series Resumes, Friday February 2

Speaker: Nikita Nekrasov (Simons Center for Geometry and Physics)
Title: The Count of Instantons
Abstract: Graduate level introduction to modern mathematical physics with the emphasis on the geometry and physics of quantum gauge theory and its connections to string theory.  We shall zoom in on a corner of the theory especially suitable for exploring non-perturbative aspects of gauge and string theory: the instanton contributions. Using a combination of methods from algebraic geometry, topology, representation theory and probability theory we shall derive a series of identities obeyed by generating functions of integrals over instanton moduli spaces, and discuss their symplectic, quantum, isomonodromic, and, more generally, representation-theoretic significance.

Quantum and classical integrable systems, both finite and infinite-dimensional ones, will be a recurring cast of characters, along with the other (qq-) characters.

Fridays at 1:30pm

Room 520 Mathematics



Lecture notes: Not split per lecture will be updated as course continues

Lecture recording

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Spring 2024 Samuel Eilenberg Lecture Series

Please join us for the Spring 2024 Samuel Eilenberg Lectures on Mondays at 4:10 p.m. in Room 520 Mathematics.

This semester, Professor Soren Galatius (University of Copenhagen), will deliver a series of lectures titled:

Moduli spaces of high dimensional manifolds

Abstract: Following influential work of John Harer in the 1980s, Ulrike Tillmann in the 1990s, and Ib Madsen and Michael Weiss in the 2000s, we learned a new approach to the moduli space of Riemann surfaces, and to the diffeomorphism groups and mapping class groups of oriented 2-manifolds.  A lesson learned by their work is that patterns emerge in the large-genus limit, another is that these patterns are well expressed in homotopy theoretic terms.

Inspired by these developments in (real) dimension 2, Oscar Randal-Williams and I set out to study moduli spaces of higher-dimensional manifolds in a similar spirit.  The goal of this semester’s Eilenberg Lectures will be to present some of our joint work, as well as some background, context, and some very recent developments in high-dimensional manifold theory building on our work.


First lecture: Monday, January 22, 2024 (weekly thereafter)

Room 520, Mathematics Hall

2990 Broadway (117th Street)





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Special Colloquium

Special Colloquium

Speaker: Tomer Schlank (Hebrew University of Jerusalem)
Title: Stable homotopy groups, higher algebra and the telescope Conjecture
Abstract: Spectra are the homotopy theorist abelian groups, they have a fundamental place in algebraic topology but also appear in arithmetic geometry, differential topology, mathematical physics and symplectic geometry. In a similar vein to the way that abelian groups are the bedrock of algebra and algebraic geometry we can take a similar approach of spectra, I will discuss the picture that emerges and how one can use it to address classical questions about homotopy groups of spheres, algebraic K-theory and cobordism classes.

Date and Time: Tuesday, January 23, 4:30 PM
Location: 407 Mathematics

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Special Colloquium

Special Colloquium

Speaker: Tom Hutchcroft (California Institute of Technology)
Title: Probability on groups
Abstract: It is a famous aphorism of Gromov that there are no non-trivial theorems that hold for all finitely generated groups. Modern probability theory has (arguably) led to several counterexamples to this claim, with a rich seam of research over the last few decades devoted to understanding the behaviour of probabilistic processes on arbitrary finitely generated groups and other homogeneous geometries. I will give an introduction to this topic, emphasizing connections to more classical topics in group theory. Time permitting, I will describe how many of the ideas developed in this field come together in my recent solution, joint with Philip Easo, of Schramm’s locality conjecture in percolation theory.

Date and Time: Friday January 26, 1:30 PM
Location: 520 Mathematics

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Abigail Hickok awarded inaugural Babuška Thesis Prize

Congratulations to Abigail Hickok, who was recently awarded the inaugural Ivo and Renata Babuška Thesis Prize!

The Babuška Prize is to be awarded annually to the author of an outstanding interdisciplinary PhD thesis in mathematics, with potential applications to other fields.

From the AMS press release:

“The inaugural Ivo and Renata Babuška Thesis Prize is awarded to Abigail Hickok in recognition of the outstanding contributions in her PhD thesis, “Topics in Geometric and Topological Data Analysis.” Hickok conducted her doctoral work at the University of California, Los Angeles (UCLA). Presently, she is an NSF postdoctoral fellow at Columbia University.”

For more information about the Babuška prize, please visit the AMS website: Ivo and Renata Babuška Thesis Prize

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Packard Foundation Grant Supports Columbia’s Efforts to Address the Under-representation of Women in Mathematics

Ivan Corwin, Professor of Mathematics and 2014 Packard Fellow in Science and Engineering, has been awarded a $40,000 award as part of the Increasing Diversity in STEM pilot program for Packard Fellows. The award will support the “Pathways for Women into Higher Mathematics” project.

The Packard Foundation’s goal in this initiative is to support Fellows’ efforts to increase the representation and inclusion of underrepresented groups (URGs) in their departments and universities.

The Pathways for Women into Higher Mathematics project will involve two pathway activities for women interested in mathematics to help guide them towards the possibilities that lay ahead in higher mathematics: the organization of the “Sonya Kovalevsky Day” for middle school aged students and a two-day Graduate Opportunities for Women (GROW) Conference to take place in 2024 and 2025.

Named after the Russian pioneer woman mathematician, the “Sonya Kovalevsky Day” will bring primarily female middle schoolers from NYC’s under-resourced schools and their teachers to Columbia to engage in hands-on workshops led by faculty and students.

The GROW Conference will bring women (cisgender, transgender, or woman-identified) and non-binary undergraduate students, primarily from non-tier I colleges or universities, to help them envision a potential career and graduate study in mathematics or statistics. GROW has been running for about 10 years, in rotating locations, and has engaged over 1,000 students over its duration.

The Packard Foundation’s support will be complemented with financial support and extensive mentorship and organizational support from the Columbia Mathematics and Statistics departments, as well as the Irving Institute for Cancer Dynamics. Corwin summed it up, saying, “these pathway activities will add to many exciting ongoing efforts at Columbia to attract a diverse population of students to higher mathematics and retain their interest and excitement.”



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In Memoriam – Henry Pinkham

With profound sadness and grief we write to share the passing of Henry Pinkham, who recently passed away. Professor Pinkham was a beloved member of the department for nearly 50 years, and also served as the Dean of the Graduate School of Arts & Sciences for 9 years. Our heartfelt condolences go out to family, friends, and colleagues. His presence in our department will be dearly missed.

In Memoriam of Professor Henry Pinkham

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