School of Mathematics

Higher order rectifiability and Reifenberg parametrizations

Silvia Ghinassi
Member, School of Mathematics
March 9, 2020
We provide geometric sufficient conditions for Reifenberg flat sets of any integer dimension in Euclidean space to be parametrized by a Lipschitz map with Hölder derivatives. The conditions use a Jones type square function and all statements are quantitative in that the Hölder and Lipschitz constants of the parametrizations depend on such a function. We use these results to prove sufficient conditions for higher order rectifiability of sets and measures.

An introduction to Boolean Function Analysis

Dor Minzer
Member, School of Mathematics
March 3, 2020
An introduction to Boolean Function Analysis
We will discuss some of the basic principles and results in the study of Boolean-valued functions over the discrete hypercube using discrete Fourier analysis. In particular, we will talk about basic concepts, the hypercontractive inequality and the KKL theorem. Time permitting, we will discuss the Fourier-Entropy Conjecture and mention some recent progress towards it.

The talk is self-contained and no special background will be assumed.

An Improved Cutting Plane Method for Convex Optimization, Convex-Concave Games and its Applications

Zhao Song
Member, School of Mathematics
March 2, 2020
Strong Average-Case Circuit Lower Bounds from Non-trivial Derandomization
We prove that, unconditionally, for all constants a, NQP = NTIME[n^polylog(n)] cannot be (1/2 + 2^(-log^a n) )-approximated by 2^(log^a n)-size ACC^0 circuits. Previously, it was even open whether E^NP can be (1/2+1/sqrt(n))-approximated by AC^0[2] circuits. As a straightforward application, we obtain an infinitely often non-deterministic pseudorandom generator for poly-size ACC^0 circuits with seed length 2^{log^eps n}, for all eps > 0.

Lower Bounds in Complexity Theory, Communication Complexity, and Sunflowers

Toniann Pitassi
University of Toronto; Visiting Professor, School of Mathematics
March 2, 2020
In this talk I will discuss the Sunflower Lemma and similar lemmas that prove (in various contexts) that a set/distribution can be partitioned into a structured part and a "random-looking" part. I will introduce communication complexity as a key model for understanding computation and more generally for reasoning about information bottlenecks.

Preference Modeling with Context-Dependent Salient Features

Laura Balzano
University of Michigan; Member, School of Mathematics
February 27, 2020
This talk considers the preference modeling problem and addresses the fact that pairwise comparison data often reflects irrational choice, e.g. intransitivity. Our key observation is that two items compared in isolation from other items may be compared based on only a salient subset of features. Formalizing this idea, I will introduce our proposal for a “salient feature preference model” and discuss sample complexity results for learning the parameters of our model and the underlying ranking with maximum likelihood estimation.

Is the variety of singular tuples of matrices a null cone?

Viswambhara Makam
February 25, 2020

The following multi-determinantal algebraic variety plays an important role in algebra and computational complexity theory: SING_{n,m}, consisting of all m-tuples of n x n complex matrices which span only singular matrices. In particular, an efficient deterministic algorithm testing membership in SING_{n,m} will imply super-polynomial circuit lower bounds, a holy grail of the theory of computation. <br>

Learning from Multiple Biased Sources

Clayton Scott
University of Michigan
February 25, 2020
When high-quality labeled training data are unavailable, an alternative is to learn from training sources that are biased in some way. This talk will cover my group’s recent work on three problems where a learner has access to multiple biased sources. First, we consider the problem of classification given multiple training data sets corrupted by label noise, and describe a weighted empirical risk minimization strategy where the weights are optimized according to the degree of corruption of each source.