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# Events for September 8, 2017 from General and Seminar calendars

## Number Theory Seminar

**Abstract:** A lattice in a Euclidean space is called extremal if it is a local maximum of the packing density function in its dimension. An old theorem of Voronoi gives a beautiful characterization of extremal lattices in terms of their geometric properties. We will review Voronoi's criterion, and then apply it to exhibit families of extremal lattices coming from some algebraic and arithmetic constructions.

## Mathematical Physics and Harmonic Analysis Seminar

**Abstract:** Deep learning (DL) is the analysis and application of a class of algorithms that in the past few years have become state of the art in a huge number of machine learning problems: playing Go, image recognition/segmentation, machine transcription/translation, to name a few. While DL works incredibly well in practice, a robust mathematical theory of why it works is still in its infancy. The purpose of this talk is to introduce one aspect of this subject. Namely, the expressive power - the ability of a approximate a rich class of functions - of deep neural nets. Some of the first theorems about this were proved in the late 80's and early 90's. I will review them, talk about some more recent work, and point to a few open questions. This talk is based in part on ongoing joint work with Mark Sellke.

## Linear Analysis Seminar

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

**Location:** BLOC 220

**Speaker:** Lenny Fukshansky, Claremont McKenna College

**Title:** *On some algebraic constructions of extremal lattices*

**URL:** *Link*

**Time:** 1:50PM - 2:50PM

**Location:** BLOC 628

**Speaker:** Boris Hanin, Texas A&M University

**Title:** *Deep Learning: Approximation Theory, Convexity, and the Expressivity of Depth in Neural Networks*

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 220

**Speaker:** Gilles Pisier, TAMU

**Title:** *Completely Sidon sets in C*-algebras*

**URL:** *Link*