Seminars and Colloquia Schedule

Group Synchronization via Cycle-Edge Message Passing

Series
Applied and Computational Mathematics Seminar
Time
Monday, March 8, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/884917410
Speaker
Gilad LermanUniversity of Minnesota

The problem of group synchronization asks to recover states of objects associated with group elements given possibly corrupted relative state measurements (or group ratios) between pairs of objects. This problem arises in important data-related tasks, such as structure from motion, simultaneous localization and mapping, Cryo-EM, community detection and sensor network localization. Two common groups in these problems are the rotation and symmetric groups. We propose a general framework for group synchronization with compact groups. The main part of the talk discusses a novel message passing procedure that uses cycle consistency information in order to estimate the corruption levels of group ratios. Under our mathematical model of adversarial corruption, it can be used to infer the corrupted group ratios and thus to solve the synchronization problem. We first explain why the group cycle consistency information is essential for effectively solving group synchronization problems. We then establish exact recovery and linear convergence guarantees for the proposed message passing procedure under a deterministic setting with adversarial corruption. We also establish the stability of the proposed procedure to sub-Gaussian noise. We further establish competitive theoretical results under a uniform corruption model. Finally, we discuss the MPLS (Message Passing Least Squares) or Minneapolis framework for solving real scenarios with high levels of corruption and noise and with nontrivial scenarios of corruption. We demonstrate state-of-the-art results for two different problems that occur in structure from motion and involve the rotation and permutation groups.

Degree conditions for Hamilton cycles

Series
Graph Theory Seminar
Time
Tuesday, March 9, 2021 - 23:30 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
Richard LangHeidelberg University

Note the unusual time!

A classic theorem of Dirac (1952) states that a graph in which every vertex is connected to half of the other vertices contains a Hamilton cycle. Over the years this result has been generalized in many interesting ways. In this talk, I will give an overview of these efforts and then explore some of the more recent developments.

Bekolle-Bonami estimates on some pseudoconvex domains

Series
Analysis Seminar
Time
Wednesday, March 10, 2021 - 02:00 for 1 hour (actually 50 minutes)
Location
Speaker
Nathan WagnerWashington University, St Louis

The Bergman projection is a fundamental operator in complex analysis. It is well-known that in the case of the unit ball, the Bergman projection is bounded on weighted L^p if and only if the weight belongs to the Bekolle-Bonami, or B_p, class. These weights are defined using a Muckenhoupt-type condition. Rahm, Tchoundja, and Wick were able to compute the dependence of the operator norm of the projection in terms of the B_p characteristic of the weight using modern tools of dyadic harmonic analysis. Moreover, their upper bound is essentially sharp. We establish that their results can be extended to a much wider class of domains in several complex variables. A key ingredient in the proof is that favorable estimates on the Bergman kernel have been obtained in these cases. This is joint work with Zhenghui Huo and Brett Wick. 

Linear multistep methods for learning dynamics

Series
School of Mathematics Colloquium
Time
Thursday, March 11, 2021 - 11:00 for 1 hour (actually 50 minutes)
Location
https://us02web.zoom.us/j/87011170680?pwd=ektPOWtkN1U0TW5ETFcrVDNTL1V1QT09
Speaker
Qiang DuColumbia University

Numerical integration of given dynamic systems can be viewed as a forward problem with the learning of unknown dynamics from available state observations as an inverse problem. The latter has been around in various settings such as the model reduction of multiscale processes. It has received particular attention recently in the data-driven modeling via deep/machine learning. Indeed, solving both forward and inverse problems forms the loop of informative and intelligent scientific computing. A natural question is whether a good numerical integrator for discretizing prescribed dynamics is also good for discovering unknown dynamics. This lecture presents a study in the context of Linear multistep methods (LMMs).

Lyapunov exponent of random dynamical systems on the circle

Series
CDSNS Colloquium
Time
Friday, March 12, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
Zoom (see add'l notes for link)
Speaker
Dominique MalicetUniversity Paris-Est Marne la vallée

Zoom link: https://zoom.us/j/97732215148?pwd=Z0FBNXNFSy9mRUx3UVk4alE4MlRHdz09

We consider a sequence of compositions of orientation preserving diffeomorphisms of the circle chosen randomly with a fixed distribution law. There is naturally associated a Lyapunov exponent, which measures the rate of exponential contractions of the sequence. It is known that under some assumptions, if this Lyapunov exponent is null then all the diffeomorphisms are simultaneously conjugated to rotations. If the Lyapunov exponent is not null but close to 0, we study how well we can approach rotations by a simultaneous conjugation. In particular, our results can apply to random products of matrices 2x2, giving quantitative versions of the classical Furstenberg theorem.

On the jump of the clique chromatic number for binomial random graphs

Series
Combinatorics Seminar
Time
Friday, March 12, 2021 - 16:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/751242993/PASSWORD (To receive the password, please email Lutz Warnke)
Speaker
Dieter MitscheInstitut Camille Jordan, Univ. de Lyon

Given a graph G, the clique chromatic number of G is the smallest number of colors needed to color the vertices of G so that no maximal clique containing at least two vertices is monochromatic.
We solve an open question proposed by McDiarmid, the speaker, and Pralat concerning the asymptotic order of the clique chromatic number for binomial random graphs.
More precisely, we find the correct order of the clique chromatic number for most values of the edge-probability p around n^{-1/2}. Furthermore, the gap between upper and lower bounds is at most a logarithmic factor in n in all cases.

Based on joint work in progress with Lyuben Lichev and Lutz Warnke.


(Please note the unusual time from 4-5pm, due to the Virtual Admitted Student Day in the School of Mathematics.)

Mathapalooza!

Series
Time
Sunday, March 14, 2021 - 13:00 for 4 hours (half day)
Location
https://2021.atlantasciencefestival.org/schedule/61
Speaker

Explore the light-hearted and artistic sides of math at Mathapalooza on the afternoon of Pi Day! There will be puzzles and games to amuse and challenge everyone from kids to rocket scientists. There will be mathematical music, magic (by Matt Baker), and artwork, and mathematical stories will be recounted on stage through dance, courtroom dramas, and circus acts.