Colloquia & Seminars

Title: Interpolation for points in $\mathbb{P}^N, N\geq 2$

Algebra Seminar Speaker: Dipendranath Mahato, Tulane University Title: Interpolation for points in $\mathbb{P}^N, N\geq 2$ Abstract: Interpolation problems study hypersurfaces in projective space passing through prescribed sets of points. Classically, one asks how many independent conditions a collection of points imposes on hypersurfaces of a fixed degree, a question that can be studied algebraically via homogeneous ideals and their Hilbert functions. In this talk, I will begin with the classical interpolation problem for reduced points and introduce the algebraic framework used to study it. I will then move to fat point schemes, where points are assigned multiplicities and hypersurfaces are required to vanish to higher order. In this setting, interpolation problems naturally lead to symbolic powers of ideals...

Title: Higgs and Coulomb branches: Geometry and Representation Theory

Member Seminar Speaker: Vasily Krylov Title: Higgs and Coulomb branches: Geometry and Representation Theory Abstract: Higgs and Coulomb branches of quiver gauge theories form two important families of Poisson varieties that are expected to be exchanged under so-called 3D mirror symmetry. Quantized Coulomb branches are associative algebras deforming the algebras of functions on Coulomb branches. They are closely related to many important representation-theoretic structures, such as Yangians, quantum groups, and Hecke algebras. In this talk, I will discuss how 3D mirror symmetry, together with other insights motivated by physics, yields very explicit answers to purely representation-theoretic questions about representations of some of these quantum groups. Talk is based on joint works with Dinkins, Karpov, Klyuev, and Lance.

Title: Higher current algebras and chiral algebras

Quantum Field Theory and Physical Mathematics Seminar Speaker: Charles Young (University of Hertfordshire) Title: Higher current algebras and chiral algebras Abstract: Vertex algebras capture physicists' notion of OPEs in chiral CFTs, in complex dimension one. For various motivations, one would like to have analogs of vertex algebras in higher dimensions. Chiral algebras, in the sense of Beilinson-Drinfeld and Francis-Gaitsgory, provide a natural framework here, because they re-express the vertex algebra axioms (which are rather sui generis, and therefore hard to generalize) as something more recognizable (a chiral algebra is a Lie algebra, of a sort). I will review this, and then go on to introduce a certain concrete model of the unit chiral algebra in higher dimensions. In higher dimensions one is forced to work up to coherent homotopy in some fashion;...

Title: Joint Math/CMSA Geometry and Quantum Theory Seminar

Joint Math/CMSA Geometry and Quantum Theory Seminar Speaker: Ahsan Khan, Harvard CMSA    

Title: Differential Geometry and Physics Seminar

Differential Geometry and Physics Seminar Speaker: François Greer, MSU

Title: Member Seminar

Member Seminar Speaker: Daniel Spiegel

Title: Compression Is All You Need: Modeling Mathematics

Freedman Seminar Speaker: Mike Freedman, Harvard CMSA Title: Compression Is All You Need: Modeling Mathematics Abstract: The talk will exposit a recent eponymous arXiv posting with coauthors Vitaly Aksenov, Eve Bodnia, and Mike Mulligan. The approach is to think like a physicist and model a seemingly complex bit of reality: mathematics, by a simple toy model where exact computations can be carried out and then compared with observation.  The models are finitely generated monoids and the data is derived from MathLib a large Lean-based repository. The hierarchical nature of definitions and lemmas in math is modeled by adding redundant generators to the monoids - think of the powers of 10 within the natural numbers which support place notation....

Title: Quantum Field Theory and Physical Mathematics

Quantum Field Theory and Physical Mathematics Seminar Speaker: Charles Young, University of Hertfordshire

Title: Colloquium

Colloquium Speaker: Ofer Feinerman, Weizmann Institute of Science    

Title: Joint Math/CMSA Geometry and Quantum Theory Seminar

Joint Math/CMSA Geometry and Quantum Theory Seminar Speaker: Lorenzo Riva, Harvard CMSA    

Title: Transcendental Epsilon Multiplicity via Divisor Volumes

Algebra Seminar Speaker: Sudipta Das, Tata Institute of Fundamental Research Title: Transcendental Epsilon Multiplicity via Divisor Volumes Abstract:  In this talk, our goal is to establish a structural bridge between asymptotic commutative algebra and transcendence theory to show that there exists an ideal in a Noetherian local ring whose epsilon multiplicity is transcendental. By equating the local-cohomological definition of epsilon multiplicity to a global divisorial volume integral on a projective bundle, we apply Baker's theorem on linear forms in logarithms to prove that the resulting arithmetic invariant falls strictly outside the field of algebraic numbers. This talk is based on collaborative work with Vinh Pham and Stephen Landsittel.  

Title: Member Seminar

Member Seminar Speaker: tba

Title: Quantum Field Theory and Physical Mathematics

Quantum Field Theory and Physical Mathematics Seminar Speaker: Surya Raghaven, Yale University

Title: Colloquium

Colloquium Speaker: Nikita Nekrasov, Simons Center  

Title: Quantum Field Theory and Physical Mathematics

Quantum Field Theory and Physical Mathematics Seminar