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Week of March 1, 2023

March 1, 2023
Colloquium [3] Structure theorems for actions of homeomorphism groups. Katie Mann - Cornell 4:10pm -
March 2, 2023
Group Actions, Geometry and Dynamics [4] Joint equidistribution of maximal flat cylinders and holonomies in Anosov homogeneous spaces Mikey Chow - Yale 4:00pm -
LOM 206
Analysis [5] Recent results in elliptic homogenization. Charles Smart - Yale University 4:00pm -
March 3, 2023
Friday Morning Seminar [6] On syzygy categories of dimer tree algebras Ralf Schiffler - UCONN 9:30am -
LOM 215
Geometric Analysis and Application [7] Intermediate curvature and a generalization of Geroch's conjecture Florian Johne - Columbia University 2:00pm -
LOM 215
March 6, 2023
Group Actions, Geometry and Dynamics [4] Arithmetic Quantum Unique Ergodicity for 3-dimensional hyperbolic manifolds Zvi Shem-Tov - IAS 4:00pm -
Geometry, Symmetry and Physics [8] Moduli of one-dimensional sheaves on P^2: cohomology, perversity, and BPS invariants Weite Pi - Yale University 4:30pm -
LOM 214
March 8, 2023
Colloquium [3] Ergodic approaches to arithmetic Ramsey theory Joel Moreira - University of Warwick 4:15pm -
LOM 214
March 9, 2023
Analysis [5] On the analyticity of the Muskat equation Jia Shi - MIT 4:00pm -
LOM 205
March 10, 2023
Friday Morning Seminar [6] Friday Morning Seminar 9:30am -
LOM 215
Geometric Analysis and Application [7] A Heintze-Karcher inequality with free boundaries and applications to capillarity theory Daniel Weser - University of Texas, Austin 2:00pm -
LOM 215
March 17, 2023
Friday Morning Seminar [6] Friday Morning Seminar 9:30am -
LOM 215
March 24, 2023
Friday Morning Seminar [6] Friday Morning Seminar 9:30am -
LOM 215
March 27, 2023
Geometry, Symmetry and Physics [8] Emergent Flattening of Moment-Curve-Like Geometries Aidan Herderschee - University of Michigan 4:30pm -
LOM 214
March 29, 2023
Colloquium [3] The arithmetic of power series and applications Yunqing Tang - UC Berkeley 4:15pm -
LOM 214
March 30, 2023
Analysis [5] Degeneration of hyperbolic surfaces and spectral gaps for large genus Xuwen Zhu - Northeastern University 4:00pm -
LOM 205
March 31, 2023
Friday Morning Seminar [6] Friday Morning Seminar 9:30am -
LOM 215

Abstracts

Week of March 1, 2023

March 1, 2023
Colloquium [3] Structure theorems for actions of homeomorphism groups. 4:10pm -
The groups Homeo(M) and Diff(M) of homeomorphisms or diffeomorphisms of a manifold M have many striking parallels with finite dimensional Lie groups.  In this talk, I’ll describe some of these, and explain joint work with Lei Chen, that gives a structure theorem for actions of homeomorphism and diffeomorphism groups on other spaces, analogous to some classical results for actions of locally compact Lie groups.  As applications, we answer many concrete questions towards classifying all actions of Diff(M) on other manifolds (many of which are nontrivial, for instance Diff(M) acts naturally on the unit tangent bundle of M…) and resolve several threads in a research program initiated by Ghys.  I’ll aim to give both a broad overview and several basic applications in the talk.
March 2, 2023
Group Actions, Geometry and Dynamics [4] Joint equidistribution of maximal flat cylinders and holonomies in Anosov homogeneous spaces 4:00pm -
LOM 206

 Margulis–Mohammadi–Oh (‘14) described the asymptotic joint equdistribution of the closed geodesics and holonomies of a geometrically finite rank one locally symmetric manifold as their lengths grow to infinity.
 We obtain an Anosov analogue of this result. More precisely,  in the quotient of a higher rank semisimple Lie group by an  Anosov subgroup, non-trivial closed orbits under a maximal real-split torus give rise to maximal flat cylinders. We prove an analogous joint equidistribution result of the maximal flat cylinders and holonomies with circumferences growing to infinity. 

This is joint work with Elijah Fromm.
Analysis [5] Recent results in elliptic homogenization. 4:00pm -

I will discuss some recent results and open problems in elliptic homogenization. This will include my work with Armstrong and Kuusi on large scale regularity for solutions of periodic operators
March 3, 2023
Friday Morning Seminar [6] On syzygy categories of dimer tree algebras 9:30am -
LOM 215

A dimer tree algebra A is the Jacobian algebra of a quiver Q (without loops and 2-cycles) with a canonical potential such that (i) every arrow lies in a chordless oriented cycle; and (ii) the dual graph is a tree. The category of non-projective syzygies over A is equivalent to the stable category of (maximal) Cohen Macaulay modules as well as to the singularity category of A. It is a triangulated 3-Calabi-Yau category.
We give a geometric model for the syzygy category for dimer tree algebras in terms of 2-diagonals in a polygon with checkerboard pattern.
This checkerboard pattern can be extended to a dimer model on the disk.
Geometric Analysis and Application [7] Intermediate curvature and a generalization of Geroch's conjecture 2:00pm -
LOM 215

In this talk we explain a non-existence result for metrics of positive m-intermediate curvature (a notion of curvature reducing to positive Ricci curvature for m =  1, and positive scalar curvature for m = n-1) on closed orientable manifolds with topology $N^n = M^{n-m} x \mathbb{T}^m$ for $n \leq 7$. Our proof uses a slicing constructed by minimization of weighted areas, the associated stability inequality, and estimates on the gradients of the weights and the second fundamental form of the slices. This is joint work with Simon Brendle and Sven Hirsch.
March 6, 2023
Group Actions, Geometry and Dynamics [4] Arithmetic Quantum Unique Ergodicity for 3-dimensional hyperbolic manifolds 4:00pm -

The Quantum Unique Ergodicity conjecture of Rudnick and Sarnak says that eigenfunctions of the Laplacian on a compact manifold of negative curvature become equidistributed as the eigenvalue tends to infinity.
In the talk I will discuss a recent work on this problem for arithmetic quotients of the three dimensional hyperbolic space. I will discuss our key result that Hecke eigenfunctions cannot concentrate on certain proper submanifolds. Joint work with Lior Silberman. 
Geometry, Symmetry and Physics [8] Moduli of one-dimensional sheaves on P^2: cohomology, perversity, and BPS invariants 4:30pm -
LOM 214

The moduli spaces of one-dimensional sheaves on P^2 are first studied by Simpson and Le Potier, and they admit a Hilbert-Chow morphism to a projective base that behaves like a completely integrable system. Following a proposal of Maulik-Toda, one expects to obtain certain BPS invariants from the perverse filtration on cohomology induced by this morphism, which motivates us to study the cohomology ring structure of these moduli spaces. In this talk, we present some recent progress on this cohomology ring, including a minimal set of tautological generators, and a “Perverse = Chern” conjecture which specializes to an asymptotic product formula for refined BPS invariants of local P^2. This can be viewed as an analogue of the recently proved P=W conjecture for Hitchin systems. Based on joint work with Junliang Shen, and with Yakov Kononov and Junliang Shen.
March 8, 2023
Colloquium [3] Ergodic approaches to arithmetic Ramsey theory 4:15pm -
LOM 214
Ramsey theory is a branch of combinatorics which seeks to find patterns in disorganized situations. One of its main achievements, Szemeredi’s theorem on arithmetic progressions, got an ergodic theoretic proof in 1977 when Furstenberg created a Correspondence Principle to encode combinatorial information about sets of integers into a dynamical system. Since then ergodic methods have been very successful in obtaining new Ramsey theoretic results, some of which still have no purely combinatorial proof.
I will survey some of the history of how ergodic theory and Ramsey theory are interconnected, leading to a recent result involving infinite sumsets.
March 9, 2023
Analysis [5] On the analyticity of the Muskat equation 4:00pm -
LOM 205

TBA
March 10, 2023
Friday Morning Seminar [6] Friday Morning Seminar 9:30am -
LOM 215

A relaxed-pace seminar on impromptu subjects related to the interests of the audience.

Everyone is welcome.

The subjects are geometry, probability, combinatorics, dynamics, and more!
Geometric Analysis and Application [7] A Heintze-Karcher inequality with free boundaries and applications to capillarity theory 2:00pm -
LOM 215

 In volume-constrained capillarity problems, minimizers may have free boundaries adhering to the container. Recent work in the study of capillarity problems has utilized stability theory for the volume-constrained isoperimetric problem to classify the shape of global minimizers and (in the case without free boundary) critical points. In this talk, I will discuss joint work with Matias Delgadino extending this program to classifying the shape of local minimizers in the presence of free boundaries.
March 17, 2023
Friday Morning Seminar [6] Friday Morning Seminar 9:30am -
LOM 215

A relaxed-pace seminar on impromptu subjects related to the interests of the audience.

Everyone is welcome.

The subjects are geometry, probability, combinatorics, dynamics, and more!
March 24, 2023
Friday Morning Seminar [6] Friday Morning Seminar 9:30am -
LOM 215

A relaxed-pace seminar on impromptu subjects related to the interests of the audience.

Everyone is welcome.

The subjects are geometry, probability, combinatorics, dynamics, and more!
March 27, 2023
Geometry, Symmetry and Physics [8] Emergent Flattening of Moment-Curve-Like Geometries 4:30pm -
LOM 214

In this talk, I discuss how an infinite dimensional convex geometry of interest to physicists exhibits "flattening," which manifests as emergent equalities among naively independent coordinates. This flattening behavior is intrinsically tied to the infinite dimensional nature of the convex geometry, as these emergent equalities only appear in the infinite dimensional limit. In more detail, the space of causal and unitary theories, called the EFT-Hedron, is identified as the intersection of a convex region given by the Minkowski sum of two moment curves and a hyperplane in an infinite dimensional projective space. I use linear programming to provide strong numeric evidence that the EFT-hedron "flattens out." For example, restricting a finite fraction of the coordinates to be even-zeta values, the remaining coordinates are (conjecturally) fixed to take odd-zeta values. I will conclude by briefly sketching how this conjecture relates to Type-I superstring theory, which corresponds to a particular point in the EFThedron.
March 29, 2023
Colloquium [3] The arithmetic of power series and applications 4:15pm -
LOM 214

Borel and Dwork gave conditions on when a nice power series with rational number coefficients comes from a rational function in terms of meromorphic convergence radii at all places. Such a criterion was used in Dwork’s proof of the rationality of zeta functions of varieties over finite fields. Later, the work of Andre, Bost and many others generalized the rationality criterion of Borel–Dwork and deduced many applications in the arithmetic of differential equations and elliptic curves. In this talk, we will discuss some further refinements and generalizations of the criteria of Andre and Bost and their applications to the unbounded denominators conjecture for modular forms, and irrationality of 2-adic zeta value at 5 and some other linear independence problems. This is joint work with Frank Calegari and Vesselin Dimitrov.
March 30, 2023
Analysis [5] Degeneration of hyperbolic surfaces and spectral gaps for large genus 4:00pm -
LOM 205

The study of "small" eigenvalues of the Laplacian on hyperbolic surfaces has a long history and has recently seen many developments. In this talk I will focus on the recent work (joint with Yunhui Wu and Haohao Zhang) on the higher spectral gaps, where we study the differences of consecutive eigenvalues up to $\lambda_{2g-2}$ for genus $g$ hyperbolic surfaces. We show that the supremum of such spectral gaps over the moduli space has infimum limit at least 1/4 as genus goes to infinity. The analysis relies on previous joint works with Richard Melrose on degenerating hyperbolic surfaces
March 31, 2023
Friday Morning Seminar [6] Friday Morning Seminar 9:30am -
LOM 215

A relaxed-pace seminar on impromptu subjects related to the interests of the audience.

Everyone is welcome.

The subjects are geometry, probability, combinatorics, dynamics, and more!
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Links
[1] https://calendar.math.yale.edu/list/calendar/grid/week/2023-W08 [2] https://calendar.math.yale.edu/list/calendar/grid/week/2023-W10 [3] https://calendar.math.yale.edu/seminars/colloquium [4] https://calendar.math.yale.edu/seminars/group-actions-geometry-and-dynamics [5] https://calendar.math.yale.edu/seminars/analysis [6] https://calendar.math.yale.edu/seminars/friday-morning-seminar [7] https://calendar.math.yale.edu/seminars/geometric-analysis-and-application [8] https://calendar.math.yale.edu/seminars/geometry-symmetry-and-physics [9] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2023-W08 [10] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2023-W10