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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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January 17: Mehtaab Sawhney (MIT)
Title: On High Girth Steiner-Triple Systems and Subspace Designs
Abstract: We discuss the recent resolutions of the 1973 conjecture of Erdős on the existence of high girth Steiner triple systems and the existence of subspace designs. The talk will focus on placing these results within the context of classical design theory and within recent advances in the absorption method in combinatorics.
Based on joint works w. Peter Keevash, Matthew Kwan, Ashwin Sah, and Michael Simkin
Time and location: Wed. Jan. 17, 4:30-5:30pm, Math 520. Tea will be served in the Math lounge at 4pm.
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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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December 6: Akhil Matthew
Title: Dieudonné theory: from classical to modern
Abstract: Dieudonné theory gives a classification in terms of “semi-linear algebra” of finite flat commutative group schemes of p-power order over a perfect field of characteristic p > 0. Over the years, Dieudonné theory has evolved in many forms (crystalline, prismatic) and recently V. Drinfeld has proposed various “Shimurian” generalizations of the theory. I will give an introduction to and overview of some of this history and more recent developments.
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November 29: Miguel Walsh

Title: Fourier uniformity of multiplicative functions

Abstract: The Fourier uniformity conjecture seeks tounderstand what multiplicative functions can have large Fourier coefficients onmany short intervals. We will discuss recent progress on this problem andexplain its connection with the distribution of prime numbers and with othercentral problems about the behaviour of multiplicative functions, such as theChowla and Sarnak conjectures.

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October 18: Maryna Viazovska (EPFL)

Speaker: Maryna Viazovska (EPFL)

Title: Random lattices with symmetries
Abstract: What is the densest lattice sphere packing in the d-dimensional Euclidean space? In this talk, we will investigate this question as the dimension goes to infinity, and we will focus on the lower bounds for the best packing density, or in other words, on the existence results. We will give a historical overview of the lower bounds proved by H. Minkowski, E. Hlawka, C. L. Siegel, C. A. Rogers, and more recently by S. Vance and A. Venkatesh. In the final part of the lecture, we will present recent work done in collaboration with V. Serban and N. Gargava on the moments of the number of lattice points in a bounded set for random lattices constructed from a number field.

Mathematics Hall, room 417 from 4:30 – 5:30pm

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October 11: Ezra Getzler

Speaker: Professor Ezra Getzler (Northwestern University)

Title: Generalizing Lie theory to higher dimensions – the De Rham theorem on simplices and cubes

Abstract: There is a generalization of Lie theory from Lie algebras to differential graded Lie algebras. Ordinary Lie theory involves first order ordinary differential equations. Higher Lie theory may be understood as a non-linear generalization of the de Rham theorem on simplicial complexes (in Dupont’s formulation), as against graphs. In this talk, we present an alternate approach to this theory, using the more elementary de Rham theorem on cubical complexes.
Along the way, we will need an interesting relationship between cubical and simplicial complexes, which has recently become better known due to its use in Lurie’s theory of straightening for infinity categories.

Mathematics Hall, room 407 from 4:30 – 5:30pm

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