Seminars Sorted by Series

In this talk, we will discuss new infinite symplectic staircases. Much recent progress has been made in the study of infinite symplectic staircases arising from embedding problems of standard ellipsoids into various symplectic four-manifolds. We...

In this talk we discuss the multiplicity question for prime closed orbits of a dynamically convex Reeb flow on the boundary of a $2n$-dimensional star-shaped domain. Our first main result asserts that such a flow has at least n prime closed Reeb...

Shuo Zhang (Morningside Center of Mathematics):Composed Dehn twist exact sequence through quilts and $(A_\infty,n)$ modules

We prove the quilted Floer cochain complexes form $(A_\infty,n)$ modules over the Fukaya category $Fuk(M \times M^-)$. Then...

We consider a class of Lagrangian sections L contained in certain Calabi-Yau Lagrangian fibrations (mirrors of toric weak Fano manifolds). We prove that a form of the Thomas-Yau conjecture holds in this case: L is Hamiltonian isotopic to a special...

Consider a symplectic surface in a three-dimensional contact manifold with boundary on Reeb orbits. We assume that the rotation numbers of the boundary Reeb orbits satisfy a certain inequality, and we also make a technical assumption that the Reeb...

The chord conjecture, due initially to Arnol'd in the case of the standard contact three-sphere, asserts the existence of a Reeb chord with boundary on every closed Legendrian submanifold of a closed contact manifold for every contact form. This...

Baptiste Serraille (ETH Zürich)On a Linear Combination of Link Spectral Invariants on the Sphere:

Link spectral invariants and their homogenizations have been defined by Cristofaro-Gardiner et.al. In joint work with Ibrahim Trifa, we define a linear...

The symplectic area of a Lagrangian submanifold L in a symplectic manifold is defined as the minimal positive symplectic area of a smooth 2-disk with boundary on L. A Lagrangian torus is called extremal if it maximizes the symplectic area among all...

The Birkhoff attractor is a closed invariant subset associated with any dissipative twist map of the annulus (of dimension 2), which was introduced by Birkhoff in 1932. We will see that it can be generalized to higher dimensions using tools from...

Julio Sampietro Christ  (Université Paris-Saclay) : Equivariant Lagrangian Non-Displacements

Lagrangian Floer theory is useful to detect non-displaceability of Lagrangian submanifolds via Hamiltonian isotopies. A related question, in the presence of...

ICM 2022 will be held virtually this year.  Please join Camillo De Lellis, Ronen Eldan, and Avi Wigderson as they give live presentations of their ICM lectures.  The schedule and abstracts are as follows:

• 1:00 PM - Camillo De Lellis, IAS
• 2:00 PM...

Thin groups are finitely generated, infinite index subgroups of arithmetic lattices in Lie groups. Interesting examples come from monodromies of families of algebraic manifolds and in these cases, the "thinness" of monodromy is explained by special...

In his study of the Baum-Connes conjecture, Vincent Lafforgue was lead to study Banach space representations of SL(n>2,F) (for F a local field) which are not by isometries but by operators of slowly growing norm. Classical tools to study unitary...

The classical Lagrange and Markov spectra encode the features of certain Diophantine approximations problems. The first systematic study of these spectra was done by Markov in 1880. Since then, these objects attracted the attention of several...

The purpose of the talk is to explain how additive combinatorics plays a role in recent work on the dimension of self-affine measures generated by maps satisfying a diophantine condition. Under low-entropy or separation assumptions, this problem is...

We show that closed negatively curved locally symmetric spaces are characterized among nearby Riemannian manifolds by the Lyapunov exponents of their geodesic flow along periodic orbits. Our methods extend to locally characterize the geodesic flows...

This talk will give a detailed introduction to the proof of Zimmer's conjecture made in recent work with Brown and Hurtado. The talk will be independent of Monday's member seminar, but I will not repeat history and motivation. I will begin by (re...

Ratner's celebrated equidistribution theorem states that the trajectory of any point in a homogeneous space under a unipotent flow is getting equidistributed with respect to some algebraic measure. In the case where the action is horospherical, one...

The "linearization" technique is a powerful method in homogeneous dynamics to control the time a unipotent orbit spends in the vicinity of a closed homogeneous subset. This method relies on the polynomial nature of a unipotent flow and does not...

Let $X \subset \R^N$ be a Borel set, $\mu$ a Borel probability measure on $X$ and $T:X \to X$ a Lipschitz and injective map. Fix $k \in \N$ greater than the (Hausdorff) dimension of $X$ and assume that the set of $p$-periodic points has dimension...

We will discuss results connecting the titular objects on infinite graphs, including some known results by Varopoulos and Coulhon and Saloff-Coste and some new resutls.

I'll try to explain what we currently understand about the theoretical power of quantum computers, in a way that's accessible to a general math and physics audience. In particular, I'll demolish the popularly-held belief that quantum computing means...

British intelligence agency MI6 in 1939 recruited English mathematician Alan Turing, portrayed by Benedict Cumberbatch, to decipher Nazi codes including Enigma codes. Turing, assisted by Joan Clarke, portrayed by Keira Knightley, worked to analyze...

Both of these talks will be useful preparation for Helmut Hofer's up coming mini-course on polyfold theory on April 4th and 5th

Both of these talks will be useful preparation for Helmut Hofer's up coming mini-course on polyfold theory on April 4th and 5th.

In recent research it has become clear that there are fascinating connections between constructive mathematics, especially as formulated in the type theory of Martin-Löf, and homotopy theory, especially in the modern treatment in terms of Quillen...

The correspondence between homotopy types and higher categorical analogs of groupoids which was first conjectured by Alexander Grothendieck naturally leads to a view of mathematics where sets are used to parametrize collections of objects without...

A "proof assistant" is a software package comprising a validity checker for proofs in a particular logic, accompanied by semi-decision procedures called "tactics" that assist the mathematician in filling in the easy parts of the proofs. I will...

The main purpose of the talk is to describe an approach for the estimate of averages over orbits of certain functions on the space of lattices. These estimates play a crucial role in the study of the distribution of values at integral points of...

In this talk I will give an overview of joint work with M. Rapoport and T. Yang on the construction of generating series whose coefficients are the classes of special divisors and 0-cycles on the arithmetic surfaces attached to Shimura curves. These...

We discuss the Kadaira-Spencer gauge theory (or BCOV theory) on Calabi-Yau geometry. We explain Givental's loop space formalism at cochain level which leads to a degenerate BV theory on Calabi-Yau manifolds. Homotopic BV quantization together with a...

Recent imaging techniques for acquiring and processing microscopic data, combined with computational models and simulations, are leading to a mechanistic understanding of the development of patterns and forms in plants. This presentation will focus...

This is a report on joint work in progress with T. Kragh, wherein we prove that a closed exact Lagrangian in a cotangent bundle is simply homotopy equivalent to the base. I will explain the two main ingredients of the proof: (i) realising the...

Let a circle act symplectically on a closed symplectic manifold $M$. If the action is Hamiltonian, we can pass to the reduced space; moreover, the fixed set largely determines the cohomology and Chern classes of $M$. In particular, symplectic circle...

An intriguing primitive representation, "expand-and-sparsify", appears in the olfactory system of the fly and the sensory systems of several other organisms. It maps an input vector to a much higher-dimensional sparse representation, using a random...