Seminars Sorted by Series

Abstract: This series will invite participants into the beautiful world of the circle method. This method, which combines both arithmetic and analytic insights, originated 100 years ago in work of Hardy and Ramanujan, in their study of the partition...

Abstract: A famous theorem of Szemeredi from 1975 states that any subset of positive density in the integers contains arbitrarily long arithmetic progressions. In 1977 Furstenberg gave an ergodic theoretic proof of Szemeredi’s theorem. Furstenberg...

Abstract: A central question in extremal graph theory is to determine ex(n,H), the maximum number of edges in a n-vertex graph containing no subgraph isomorphic to some forbidden graph H. One may define a topological variant of this extremal...

Abstract: I will discuss how the Bentkus-Götze-Freeman variant of the Davenport-Heilbronn circle method can be used to study $\mathbb{F}_q[t]$ solutions to inequalities of the form $$\text{ord}(\lambda_1 x_1^k + \cdots + \lambda_s x_s^k - \tau) ...

Abstract: In 2016 Bourgain applied Gauss sums to construct a counterexample related to a decades-old question in PDEs. The story started in 1980 when Carleson asked about how “smooth" an initial data function must be to imply pointwise convergence...

Abstract: This series will invite participants into the beautiful world of the circle method. This method, which combines both arithmetic and analytic insights, originated 100 years ago in work of Hardy and Ramanujan, in their study of the partition...

Abstract: A famous theorem of Szemeredi from 1975 states that any subset of positive density in the integers contains arbitrarily long arithmetic progressions. In 1977 Furstenberg gave an ergodic theoretic proof of Szemeredi’s theorem. Furstenberg...

Abstract: Every infinite sequence on a finite set of symbols gives rise to a dynamical system by taking the topological closure of the set of iterates of the sequence under the shift map, which deletes the first symbol of a sequence. Given any...

Abstract: Complex dynamics explores the evolution of points under iteration of functions of complex variables. In this talk I will describe an interesting phenomenon in complex dynamics called wandering domains. I will mention a few techniques used...

Abstract: In 1985, Maier demonstrated that there are short intervals with an exceptionally large or small number of primes. In this talk, I will discuss an analog of this result for primes in three-term and four-term arithmetic progressions. I aim...

Abstract: This series will invite participants into the beautiful world of the circle method. This method, which combines both arithmetic and analytic insights, originated 100 years ago in work of Hardy and Ramanujan, in their study of the partition...

Abstract: A famous theorem of Szemeredi from 1975 states that any subset of positive density in the integers contains arbitrarily long arithmetic progressions. In 1977 Furstenberg gave an ergodic theoretic proof of Szemeredi’s theorem. Furstenberg...

Abstract: This series will invite participants into the beautiful world of the circle method. This method, which combines both arithmetic and analytic insights, originated 100 years ago in work of Hardy and Ramanujan, in their study of the partition...

Abstract: A famous theorem of Szemeredi from 1975 states that any subset of positive density in the integers contains arbitrarily long arithmetic progressions. In 1977 Furstenberg gave an ergodic theoretic proof of Szemeredi’s theorem. Furstenberg...

Abstract: Some of the most important problems in combinatorial number theory ask for the size of the largest subset of the integers in an interval lacking points in a fixed arithmetically defined pattern. One example of such a problem is to prove...

Abstract: Geometry and representation theory are intertwined in deep and foundational ways. One of the most important instances of this relationship was uncovered in the 1970s by Deligne and Lusztig: the representation theory of matrix groups over...

Abstract: The goal of this lecture series is to give you a glimpse into the Langlands program, a central topic at the intersection of algebraic number theory, algebraic geometry and representation theory. In the first lecture, we will look at a...

Abstract: How fast do Betti numbers grow in a congruence tower of covering spaces? I'll discuss this question in the special case of Picard modular surfaces, which are 4-dimensional real manifolds. There, the question is most interesting in degree 1...

Abstract: The Emerton-Gee stack is a stack of etale $\phi$ modules, and can be viewed as a stack of p-adic representations for the Galois group of a finite extension $K$ of $Qp$. In this talk, we will introduce the stack and talk about its role in...

Abstract: Geometry and representation theory are intertwined in deep and foundational ways. One of the most important instances of this relationship was uncovered in the 1970s by Deligne and Lusztig: the representation theory of matrix groups over...

Abstract: The goal of this lecture series is to give you a glimpse into the Langlands program, a central topic at the intersection of algebraic number theory, algebraic geometry and representation theory. In the first lecture, we will look at a...

Abstract: An explicit understanding of the category of all (smooth, complex) representations of p-adic groups provides an important tool not just within representation theory. It also has applications to number theory and other areas, and in...

Abstract: Geometry and representation theory are intertwined in deep and foundational ways. One of the most important instances of this relationship was uncovered in the 1970s by Deligne and Lusztig: the representation theory of matrix groups over...

Abstract: The goal of this lecture series is to give you a glimpse into the Langlands program, a central topic at the intersection of algebraic number theory, algebraic geometry and representation theory. In the first lecture, we will look at a...

Shimura varieties are an important geometric object in the Langlands program, because the Hecke (adelic group) action allows us to view various cohomology groups as Hecke modules. Moreover, the cohomology admits an integral structure when the...

Abstract: The theory of elliptic curves with complex multiplication has yielded some striking arithmetic applications, ranging from (cases of) Hilbert’s Twelfth Problem to the Birch and Swinnerton-Dyer Conjecture. These applications rely on the...

Abstract: Geometry and representation theory are intertwined in deep and foundational ways. One of the most important instances of this relationship was uncovered in the 1970s by Deligne and Lusztig: the representation theory of matrix groups over...

Abstract: The goal of this lecture series is to give you a glimpse into the Langlands program, a central topic at the intersection of algebraic number theory, algebraic geometry and representation theory. In the first lecture, we will look at a...

Come play with 250 physical wooden blocks and join us in thinking about a simple open problem for dimers in 3D. No prior knowledge required. We’ll start with an ~10 minute presentation explaining the problem and then suggest some things for everyone...

History of the math

This talk will present some theorems and conjectures about the spectral properties of large random matrices and its connection to spin systems with hyperbolic symmetry.

Abstract:  I will survey recent progress on understanding the value distribution of zeta and L-functions.  In particular I will discuss the problem of moments of the zeta function on the critical line, and central  values of L-functions, where the...

Large sieve inequalities are useful and flexible tools for understanding families of L-functions.  The quality of the bound is one measure of our understanding of the corresponding family.  For instance, they may directly give rise to good bounds...

Abstract: Multiplicative chaos is the general name for a family of probabilistic objects, which can be thought of as the random measures obtained by taking the exponential of correlated Gaussian random variables. Multiplicative chaos turns out to be...

I will give an introduction to Gaussian multiplicative chaos and some of its applications, e.g. in Liouville theory. Connections to random matrix theory and number theory will also be briefly discussed.

Rank-one non-Hermitian deformations of  tridiagonal beta-Hermite Ensembles have been introduced by R. Kozhan several years ago. For a fixed N and beta>0 the joint probability density of N complex eigenvalues  was shown to have a form of a...

In 2012, Fyodorov, Hiary & Keating and Fyodorov & Keating proposed a series of conjectures describing the statistics of large values of zeta in short intervals of the critical line. In particular, they relate these statistics to the ones of log...

Selberg’s celebrated central limit theorem shows that the logarithm of the zeta function at a typical point on the critical line behaves like a complex, centered Gaussian random variable with variance $\log\log T$. This talk will present recent...