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# Events for 11/20/2019 from all calendars

## Inverse Problems and Machine Learning

## Mathematical Physics and Harmonic Analysis Seminar

## Noncommutative Geometry Seminar

## Numerical Analysis Seminar

## Graduate Student Organization Seminar

**Time:** 12:00PM - 1:00PM

**Location:** BLOC 628

**Speaker:** David Rolnick, UPenn

**Title:** *Identifying Weights and Architectures of Unknown ReLU Networks*

**Abstract:** The output of a neural network depends on its parameters in a highly nonlinear way, and it is widely assumed that a network's parameters cannot be identified from its outputs. Here, we show that in many cases it is possible to reconstruct the architecture, weights, and biases of a deep ReLU network given the ability to query the network. ReLU networks are piecewise linear and the boundaries between pieces correspond to inputs for which one of the ReLUs switches between inactive and active states. Thus, first-layer ReLUs can be identified (up to sign and scaling) based on the orientation of their associated hyperplanes. Later-layer ReLU boundaries bend when they cross earlier-layer boundaries and the extent of bending reveals the weights between them. Our algorithm uses this to identify the units in the network and weights connecting them (up to isomorphism). The fact that considerable parts of deep networks can be identified from their outputs has implications for security, neuroscience, and our understanding of neural networks. Joint work with Konrad Körding.

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

**Location:** BLOC 624

**Speaker:** Rodrigo Bezerra Matos, MSU

**Title:** *Localization in the disordered Hubbard model within Hartree-Fock theory*

**Abstract:** After a brief and self-contained review of the results on Anderson localization in the non-interacting setting, we shall discuss recent developments on the interacting context. This will be done for the disordered Hubbard model within the Hartree-Fock theory, which is an approximation used to understand qualitatively the time evolution of a particle subject not only to a random environment but also to infinitely many interactions. There, we prove (single particle) localization at any dimension in the regime of large disorder and at any disorder in the one-dimensional case. This is joint work with Jeffrey Schenker.

**Time:** 2:00PM - 3:00PM

**Location:** BLOC 628

**Speaker:** Peter Hochs, University of Adelaide

**Title:** *A localised equivariant index for proper actions and an APS index theorem.*

**Abstract:** Roe defined a localised version of the coarse index of an elliptic operator that is invertible outside a subset Z of the manifold M it is defined on. An equivariant version of this index was defined for proper and free actions by discrete groups by Xie and Yu. With Guo and Mathai, we extended this to proper actions by any locally compact group G. If Z/G is compact, then this index takes values in the K-theory of the group C* algebra of G, and generalises the Baum-Connes analytic assembly map. It also generalises an equivariant index of Callias-type operators constructed earlier by Guo. Another special case is an equivariant index for proper, cocompact actions on manifolds with boundary, generalising the Atiyah-Patodi-Singer (APS) index and its equivariant version. With Bai-Ling Wang and Hang Wang, we obtained an equivariant APS index theorem in this context. Using a version for maximal group C*-algebras and Roe algebras, we obtain a link with an index on invariant sections defined earlier with Mathai.

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

**Location:** BLOC 628

**Speaker:** Gunnar Martinsson, UT Austin

**Title:** *Randomized algorithms for large scale linear algebra*

**Abstract:** The task of solving large scale linear algebraic problems such as factorizing matrices or solving linear systems is of central importance in many areas of scientific computing, as well as in data analysis and computational statistics. The talk will describe how randomization can be used to design algorithms that in many environments have both better asymptotic complexities and better practical speed than standard deterministic methods.

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

**Location:** BLOC 628

**Speaker:** C.J. Bott

**Title:** *Why An Algebraist's Favorite Subject Should be Calculus*

**Abstract:** A traditional undergraduate abstract algebra course focuses on groups (which have 1 binary operation) and rings (which have 2 binary operations), but the fact is that there are many more algebraic structures (with 1,2, or more than 2 binary operations) that are ubiquitous in mathematics. In this talk, I will introduce the simplest forms of my two favorite examples of algebraic structures: smooth functions and smooth vector fields in \mathbb{R}^n! While many may be familiar with these sets from calculus, they have an astounding number of binary operations with immediate and interesting geometric consequences. It is my hope that mathematicians of all backgrounds will enjoy seeing these connections in math that are not usually taught in a formal course.

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