Seminars Sorted by Series

The basic ingredients of Darwinian evolution, selection and mutation, are very well described by simple mathematical models. In 1973, John Maynard Smith linked game theory with evolutionary processes through the concept of evolutionarily stable...

I will survey the development of modern infinite cardinal arithmetic, focusing mainly on S. Shelah's algebraic pcf theory, which was developed in the 1990s to provide upper bounds in infinite cardinal arithmetic and turned out to have applications...

I will introduce two basic problems in random geometry. A self-avoiding walk is a sequence of steps in a d-dimensional lattice with no self-intersections. If branching is allowed, it is called a branched polymer. Using supersymmetry, one can map...

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I will start with a review the basic notions of Hamiltonian/symplectic vector field and of Hamiltonian/symplectic group action, and the classical structure theorems of Kostant, Atiyah, Guillemin-Sternberg and Delzant on Hamiltonian torus actions...

Let f and g be nonlinear polynomials (in one variable) over the complex numbers. I will show that, if there exist complex numbers a and b for which the orbits {a, f(a), f(f(a)), ...} and {b, g(b), g(g(b)), ...} have infinite intersection, then f and...

The modern theory of dynamical systems, as well as symplectic geometry, have their origin with Poincare as one field with integrated Ideas. Since then these fields developed quite independently. Given the progress in these fields one can make a good...

A Lagrangian correspondence is a Lagrangian submanifold in the product of two symplectic manifolds. This generalizes the notion of a symplectomorphism and was introduced by Weinstein in an attempt to build a symplectic category. In joint work with...

It is becoming more and more clear that many of the most exciting structures of our world can be described as large networks. The internet is perhaps the foremost example, modeled by different networks (the physical internet, a network of devices...

I will describe the notions of strong and weak epsilon nets in range spaces, and explain briefly some of their many applications in Discrete Geometry and Combinatorics, focusing on several recent results in the investigation of the extremal...

This is the talk I gave in Frankfurt which was organized to commemorate the 100th birthday of Theodor Schneider. He and, independently, A. Gelfond gave in 1934 two different solutions to Hilbert's 7th problem. We shall give a historical panorama of...

Bordered Floer homology is an invariant for three-manifolds with boundary (or, more precisely, three-manifolds with parameterized boundary), constructed using pseudo-holomorphic curve techniques. The theory associates to a marked surface a...

A metric on a compact manifold M gives rise to a length function on the free loop space LM whose critical points are the closed geodesics on M in the given metric. Morse theory gives a link between Hamiltonian dynamics and the topology of loop...

Pseudo-holomorphic curves play a fundamental role in the study of symplectic manifolds. Compactness and gluing theorems allow to extract algebra out of analysis. The focus of this talk are certain invariants which are constructed using pseudo...

This talk will review some theorems and conjectures about phase transitions of interacting spin systems in statistical mechanics. A phase transition may be thought of as a change in a typical spin configuration from ordered state at low temperature...

A classical theorem of Dirichlet establishes the existence of infinitely many primes in arithmetic progressions, so long as there are no local obstructions. In 2006 Green and Tao set up a program for proving a vast generalization of this theorem...

Enumerative geometry is a classical subject often concerned with enumeration of complex curves of various types in projective manifolds under suitable regularity conditions. However, these conditions rarely hold. On the other hand, Gromov-Witten...

Andrei Rapinchuk and I have introduced a new notion of ``weak-commensurability’’ of subgroups of two semi-simple groups. We have shown that existence of weakly-commensurable Zariski-dense subgroups in semi-simple groups G_1 and G_2 lead to strong...

A classical theorem in Euclidean geometry asserts that if a set of points has the property that every line through two of them contains a third point, then they must all be on the same line. We prove several approximate versions of this theorem (and...

My goal in this talk is to survey some of the emerging applications of polynomial methods in both learning and in statistics. I will give two examples from my own work in which the solution to well-studied problems in learning and statistics can be...

Part of geometric representation theory involves constructing representations of algebras on the cohomology of algebraic varieties. A great example of such a construction is the work of Nakajima and Grojnowski, who independently constructed an...

Heegaard Floer homology groups were recently introduced by Ozsvath and Szabo to study properties of 3-manifolds and knots in them. The definition of the invariants rests on delicate holomorphic geometry, making the actual computations cumbersome. In...

I will give an introduction to the problem of parallel repetition of two-prover games and its applications and related results in theoretical computer science (the PCP theorem, hardness of approximation), mathematics (the geometry of foams, tiling...

I will give an introduction to symplectic geometry and Hamiltonian systems and then introduce an invariant called symplectic cohomology. This has many applications in symplectic geometry and has been used a lot especially in the last 5-10 years. I...

Quillen's higher K-groups, defined in 1971, paved the way for motivic cohomology of algebraic varieties. Their definition as homotopy groups of combinatorially constructed topological spaces initially seems abstract and inaccessible. In this talk...

Patching methods are usually used to construct global objects from more local ones. On the other hand, algebraic objects can sometimes be understood from their local behavior, i.e., they satisfy a local-global principle. In this talk, we explain a...

35 years ago Wehrl defined a classical entropy of a quantum density matrix using Gaussian (Schr\"odinger, Bargmann, ...) coherent states. This entropy, unlike other classical approximations, has the virtue of being positive. He conjectured that the...

This talk is intended for a general audience. The recent discovery of an interpretation of constructive type theory into abstract homotopy theory has led to a new approach to foundations with both intrinsic geometric content and a computational...

This talk is designed for a general mathematical audience; no prior knowledge of type theory is presumed. One of the main goals for the special year on univalent foundations is the development of a logical formalism, called homotopy type theory...

A general algebraic formalism for the mathematical modeling of physical systems is sketched. This formalism is sufficiently general to encompass classical and quantum-mechanical models. It is then explained in which way quantum theory differs in an...

A `toy model' for studying the probabilistic distribution of nodal curves of eigenfunctions of linear operators arises from the Laplacian on the standard real 2-torus. Here the eigenvalues are associate to integers m that are sum of two squares...

This is the first of two talks in which the speaker will discuss the development of the theory of Toeplitz matrices and determinants in response to questions arising in the analysis of the Ising model of statistical mechanics. The first talk will be...

``Quantum ergodicity'' usually deals with the study of eigenfunctions of the Laplacian on Riemannian manifolds, in the high-frequency asymptotics. The rough idea is that, under certain geometric assumptions (like negative curvature), the...

Mirror symmetry is a deep conjectural relationship between complex and symplectic geometry. It was first noticed by string theorists. Mathematicians became interested in it when string theorists used it to predict counts of curves on the quintic...

Fundamental questions in basic and applied ecology alike involve complex adaptive systems, in which localized interactions among individual agents give rise to emergent patterns that feed back to affect individual behavior. In such systems, a...