Calendar

Suppose A is a subset of the natural numbers with positive density. A classical result in additive combinatorics, Szemeredi’s theorem, states that for each positive integer k, A must have an arithmetic progression of nonzero common difference of length k.

In this talk, we shall discuss various quantitative refinements of this theorem and explain the various ingredients that recently led to the best quantitative bounds for this theorem. This is joint work with Ashwin Sah and Mehtaab Sawhney.

===============================

For more info, see https://math.mit.edu/combin/

Suppose A is a subset of the natural numbers with positive density. A classical result in additive combinatorics, Szemeredi’s theorem, states that for each positive integer k, A must have an arithmetic progression of nonzero common difference of length k.

In this talk, we shall discuss various quantitative refinements of this theorem and explain the various ingredients that recently led to the best quantitative bounds for this theorem. This is joint work with Ashwin Sah and Mehtaab Sawhney.

===============================

For more info, see https://math.mit.edu/combin/

For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar

Suppose A is a subset of the natural numbers with positive density. A classical result in additive combinatorics, Szemeredi’s theorem, states that for each positive integer k, A must have an arithmetic progression of nonzero common difference of length k.

In this talk, we shall discuss various quantitative refinements of this theorem and explain the various ingredients that recently led to the best quantitative bounds for this theorem. This is joint work with Ashwin Sah and Mehtaab Sawhney.

===============================

For more info, see https://math.mit.edu/combin/

Suppose A is a subset of the natural numbers with positive density. A classical result in additive combinatorics, Szemeredi’s theorem, states that for each positive integer k, A must have an arithmetic progression of nonzero common difference of length k.

In this talk, we shall discuss various quantitative refinements of this theorem and explain the various ingredients that recently led to the best quantitative bounds for this theorem. This is joint work with Ashwin Sah and Mehtaab Sawhney.

===============================

For more info, see https://math.mit.edu/combin/

Let $E/\mathbb{Q}$ be an elliptic curve of analytic rank $2$, and let $p$ be an odd prime of good, ordinary reduction such that the $p$-torsion of $E(\mathbb{Q})$ is trivial. Let $K$ be an imaginary quadratic field satisfying the Heegner hypothesis for $E$ and such that the analytic rank of the twisted curve $E^K/\mathbb{Q}$ is $1$. Further suppose that $p$ splits in $\mathcal{O}_K$. Under these assumptions, there is a $1$-dimensional $\mathbb{Q}_p$-vector space attached to the triple $(E, p, K)$, known as the shadow line, and it can be computed using anticyclotomic $p$-adic heights. We describe the computation of these heights and shadow lines. Furthermore, fixing pairs $(E, p)$ and varying $K$, we present some data on the distribution of these shadow lines. This is joint work with Mirela Çiperiani, Barry Mazur, and Karl Rubin.

For more info, see https://ashvin-swaminathan.github.io/home/NTSeminar.html

Let (W,S) be a Coxeter system, and write S={s_i : i is in I}, where I is a finite index set. Consider a nonempty finite convex subset L of W. If W is a symmetric group, then L is the set of linear extensions of a poset, and there are important Bender–Knuth involutions BK_i (indexed by I) defined on L. For arbitrary W and for each i in I, we introduce an operator \tau_i on W that we call a noninvertible Bender–Knuth toggle; this operator restricts to an involution on L that coincides with BK_i when W is a symmetric group. Given an ordering i_1,…,i_n of I and a starting element u_0 of W, we can repeatedly apply the toggles in the order \tau_{i_1},…,\tau_{i_n},\tau_{i_1},…,\tau_{i_n},…. This produces a sequence of elements of W that can be viewed in terms of a beam of light that bounces around in an arrangement of transparent windows and one-way mirrors. Our central questions concern whether or not the beam of light eventually ends up in the convex set L. We will discuss several situations where this occurs and several situations where it does not. This is based on joint work with Grant Barkley, Eliot Hodges, Noah Kravitz, and Mitchell Lee.

===============================

For more info, see https://math.mit.edu/combin/

Suppose A is a subset of the natural numbers with positive density. A classical result in additive combinatorics, Szemeredi’s theorem, states that for each positive integer k, A must have an arithmetic progression of nonzero common difference of length k.

In this talk, we shall discuss various quantitative refinements of this theorem and explain the various ingredients that recently led to the best quantitative bounds for this theorem. This is joint work with Ashwin Sah and Mehtaab Sawhney.

===============================

For more info, see https://math.mit.edu/combin/

In collider physics, perturbative quantum field theory is the workhorse framework for computing theoretical predictions to compare to experimental measurements. An observable is called “safe” if its cross section can be predicted order-by-order in perturbation theory with controlled non-perturbative corrections. In this talk, I show that naive definitions of “safety” are inadequate to determine which observable are perturbatively calculable. I then argue for a more refined definition of safety based on principles from optimal transport theory.

Zoom: https://harvard.zoom.us/j/977347126

Password: cmsa

Recently, there has been much progress in understanding stationary measures for colored (also called multi-species or multi-type) interacting particle systems, motivated by asymptotic phenomena and rich underlying algebraic and combinatorial structures (such as nonsymmetric Macdonald polynomials).

In this work, we present a unified approach to constructing stationary measures for several colored particle systems on the ring and the line, including (1) the Asymmetric Simple Exclusion Process (mASEP); (2) the q-deformed Totally Asymmetric Zero Range Process (TAZRP) also known as the q-Boson particle system; (3) the q-deformed Pushing Totally Asymmetric Simple Exclusion Process (q-PushTASEP). Our method is based on integrable stochastic vertex models and the Yang–Baxter equation. We express the stationary measures as partition functions of new “queue vertex models” on the cylinder. The stationarity property is a direct consequence of the Yang–Baxter equation. This is joint work with A. Aggarwal and L. Petrov.

===============================

For more info, see https://math.mit.edu/combin/

Suppose A is a subset of the natural numbers with positive density. A classical result in additive combinatorics, Szemeredi’s theorem, states that for each positive integer k, A must have an arithmetic progression of nonzero common difference of length k.

In this talk, we shall discuss various quantitative refinements of this theorem and explain the various ingredients that recently led to the best quantitative bounds for this theorem. This is joint work with Ashwin Sah and Mehtaab Sawhney.

===============================

For more info, see https://math.mit.edu/combin/

Knot Floer homology is a powerful invariant of knots and links, developed by Ozsvath and Szabo in the early 2000s. Among other properties, it detects the genus, detects fiberedness, and gives a lower bound to the 4-ball genus. The original definition involves counting homomorphic curves in a high-dimensional manifold, and as a result the invariant can be hard to compute. In 2007, Manolecu, Ozsvath, and Sarkar came up with a purely combinatorial description of knot Floer homology for knots in the 3-sphere, called grid homology. Soon after, Ozsvath, Szabo, and Thurston defined invariants of Legendrian knots using grid homology. We show that the filtered version of these GRID invariants, and consequently their associated invariants in a certain spectral sequence for grid homology, obstruct decomposable Lagrangian cobordisms in the symplectization of the standard contact structure, strengthening a result of Baldwin, Lidman, and Wong. This is joint work with Jubeir, Schwartz, Winkeler, and Wong.

Suppose A is a subset of the natural numbers with positive density. A classical result in additive combinatorics, Szemeredi’s theorem, states that for each positive integer k, A must have an arithmetic progression of nonzero common difference of length k.

In this talk, we shall discuss various quantitative refinements of this theorem and explain the various ingredients that recently led to the best quantitative bounds for this theorem. This is joint work with Ashwin Sah and Mehtaab Sawhney.

===============================

For more info, see https://math.mit.edu/combin/