Calendar

Recently there has been lots of activity surrounding generalized notions of symmetry in quantum field theory, including “categorical symmetries”, “higher symmetries”, “noninvertible symmetries”, etc. Inspired by definitions of abstract (finite) groups and algebras and their linear actions, we introduce a framework for these symmetries in field theory and a calculus of topological defects based on techniques in topological field theory.  This is joint work with Constantin Teleman and Greg Moore.

For information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/quantum-matter-seminar/

I’ll discuss a number of interactions between algebraic geometry, low-dimensional topology, and arithmetic, arising from the study of local systems on moduli spaces of curves. I’ll explain how, in joint work with Aaron Landesman, we exploit these connections to resolve open questions of Prill, Esnault-Kerz, and others.

An automorphic form can appear in multiple degrees of the cohomology of arithmetic manifolds, and this happens mostly when the arithmetic manifolds are not algebraic. This phenomenon is a part of the “derived” structures of the Langlands program, suggested by Venkatesh. However, even over algebraic arithmetic manifolds, certain automorphic forms like weight-one elliptic modular forms possess a derived structure. In this talk, we discuss this idea over Shimura varieties. A part of the story is the construction of archimedean/p-adic “derived” operators on the cohomology of Shimura varieties, using complex/p-adic Hodge theory.

Based on a joint work with Paul Bourgade.

Based on a joint work with Paul Bourgade.

This seminar will be held in Science Center 530 at 4:00pm on Wednesday, November 9th.

Please see the seminar page for more details: https://www.math.harvard.edu/~ctm/sem

A hyperplane arrangement of braid type is a collection of hyperplanes in R^n of the form {x_i-x_j=s}, where i,j are indices in [n] and s is an integer. Classical families include the Catalan, Shi, Semi-order and Linial arrangements. In this talk we will discuss some bijections between the regions of braid type arrangements and some labeled plane trees. This bijective framework applies to the braid type arrangements which satisfy a particular property that we call “transitivity” (the above classical families are all transitive). Time permitting we will then discuss some recent progress in extending this bijective framework in two directions: (a) extension of the bijections to lower dimensional faces, and (b) extension to arrangements of other Coxeter types (which include hyperplanes of the form {x_i+x_j=s}). Part of this work is joint with Te Cao.

Title: TBA

Abstract: TBA

We present large classes of non-extremal solitons in gravity that are asymptotic to four-dimensional Minkowski spacetime plus extra compact dimensions. They correspond to smooth horizonless geometries induced by topology in spacetime and supported by electromagnetic flux, which characterize coherent states of quantum gravity. We discuss a new approach to deal with Einstein-Maxwell equations in more than four dimensions, such that they decompose into a set of Ernst equations. We generate the solitons by applying different techniques associated with the Ernst formalism. We focus on solitons with zero net charge yet supported by flux, and compare them to Schwarzschild black holes. These are also ultra-compact geometries with very high redshift but differ in many aspects. At the end of the talk, we discuss the stability properties of the solitons and their gravitational signatures.

This seminar will be held over Zoom. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event/general-relativity-2021-22/

A link of an isolated complex surface singularity (X, 0) is a 3-manifold Y which is the boundary of the intersection of X with a small ball centered at 0. Smoothings of the singularity give non-singular 4-manifolds, the Milnor fibers, with the same boundary Y. The Milnor fibers carry symplectic (even Stein) structures, and thus provide fillings of the canonical contact structure on Y; another Stein filling comes from the minimal resolution of (X, 0). An important question is whether all Stein fillings of the link come from this algebraic construction: this is true in some simple cases such as lens spaces. However, even in the “next simplest” case, for many rational singularities, we are able to construct “unexpected” Stein fillings that do not arise from Milnor fibers. To this end, we encode Stein fillings via curve arrangements, motivated by  T.de Jong-D.van Straten’s description of smoothings  of certain rational surface singularities in terms of deformations of associated singular plane curves. We then use classical projective geometry  to construct unexpected line arrangements and unexpected fillings. This is a topological story, with minimal input from algebraic geometry.  Joint work with L. Starkston.