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# Events for 04/23/2021 from all calendars

## Noncommutative Geometry Seminar

## Mathematical Physics and Harmonic Analysis Seminar

## Algebra and Combinatorics Seminar

**Time: ** 1:00PM - 2:00PM

**Location: ** Zoom 951 5490 42

**Speaker: **Ieke Moerdijk, Utrecht University

**Title: ***An Introduction to Dendroidal Topology*

**Abstract: **Simplicial sets form a classical and well known tool for modelling topological spaces, and more recently topologically enriched categories and infinity categories. I will present an extension of the category of simplicial sets, called “dendroidal sets”, and explain how these can model topological operads and their algebras. The definition is based on a simple category of trees, and the goal of the talk will be to give a leisurely introduction to dendroidal sets and some of their uses. Applications include an efficient infinite loop space machine, the analysis of derived mapping spaces of E_n operads, and Koszul duality, for example.
The talk will be based on work with or by many people, among whom Boavida, Cisinski, Goeppl, Heuts, Hinich, Weiss, and others.

**URL: ***Event link*

**Time: ** 2:00PM - 2:50PM

**Location: ** Zoom

**Speaker: **Jason Metcalfe, University of North Carolina at Chapel Hill

**Title: ***Local energy in the presence of degenerate trapping*

**Abstract: **Trapping is a known obstruction to local energy estimates for the wave equation and local smoothing estimates for the Schrödinger equation. When this trapping is sufficiently unstable, it is known that estimates with a logarithmic loss can be obtained. On the other hand, for very stable trapping, it is known that all but a logarithmic amount of local energy decay is lost. Until somewhat recently, explicit examples of scenarios where an algebraic loss (of regularity) was both necessary and sufficient for local energy decay had not be constructed. We will review what is known in these specific examples. We will also examine the relationship between the trapping and the existence of a boundary. In this highly symmetric case, a relatively simple proof showing a bifurcation in the behavior of local energy as the boundary passes through the trapping is available. This is related, e.g., to the instability of ultracompact neutrino stars.

**Time: ** 3:00PM - 4:00PM

**Location: ** Zoom

**Speaker: **Byeongsu Yu, TAMU

**Title: ***When is the quotient of a semigroup ring by a monomial ideal Cohen-Macaulay?*

**Abstract: **We give a new combinatorial criterion for quotients of affine semigroup rings by monomial ideals to be Cohen-Macaulay, by computing the homology of finitely many polyhedral complexes. This provides a common generalization of well-known criteria for affine semigroup rings and monomial ideals in polynomial rings. This is joint work with Laura Matusevich.