Home » Articles posted by NS Added on February 20, 2024 by NSCongratulations 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: https://sloan.org/fellowships
The full list of 2024 recipients, including two other Columbia faculty, is available at https://sloan.org/fellowships/2024Fellows, and an official press release from Columbia can be read here https://news.columbia.edu/news/threecolumbiafacultymembersnamedsloanresearchfellows.
Print this pageAdded on February 07, 2024 by NSSpeaker: 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 threesphere. In the orientable case, surfaces of every genus can be minimally embedded. In the nonorientable 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 threefolds 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
 How does one deal with a partial differential equation when there is no natural operator?
 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?
 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)
Flyer
Print this pageAdded on January 31, 2024 by NSSpecial 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
Print this pageAdded on January 26, 2024 by NSSpecial 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 nonperturbative 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, representationtheoretic significance.
Quantum and classical integrable systems, both finite and infinitedimensional ones, will be a recurring cast of characters, along with the other (qq) characters.
Fridays at 1:30pm
Room 520 Mathematics
Flyer
Notes
Lecture notes: Not split per lecture will be updated as course continues
Lecture recording
Print this pageAdded on January 22, 2024 by NSPlease 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 2manifolds. A lesson learned by their work is that patterns emerge in the largegenus limit, another is that these patterns are well expressed in homotopy theoretic terms.
Inspired by these developments in (real) dimension 2, Oscar RandalWilliams and I set out to study moduli spaces of higherdimensional 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 highdimensional manifold theory building on our work.
First lecture: Monday, January 22, 2024 (weekly thereafter)
Room 520, Mathematics Hall
2990 Broadway (117th Street)
Flyer
Print this pageAdded on January 22, 2024 by NSSpecial 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 Ktheory and cobordism classes.
Date and Time: Tuesday, January 23, 4:30 PM
Location: 407 Mathematics
Print this pageAdded on January 22, 2024 by NSSpecial Colloquium
Speaker: Tom Hutchcroft (California Institute of Technology)
Title: Probability on groups
Abstract: It is a famous aphorism of Gromov that there are no nontrivial 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
Print this pageAdded on November 22, 2023 by NSCongratulations 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
Print this pageAdded on July 20, 2023 by NSIvan 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 twoday 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 underresourced schools and their teachers to Columbia to engage in handson workshops led by faculty and students.
The GROW Conference will bring women (cisgender, transgender, or womanidentified) and nonbinary undergraduate students, primarily from nontier 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.”
Print this pageAdded on July 05, 2023 by NSWith 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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