Seminars and Colloquia by Series

TBA James Conway

Series
Geometry Topology Seminar
Time
Monday, December 9, 2019 - 14:30 for 1 hour (actually 50 minutes)
Location
Skiles 202
Speaker
James ConwayUC, Berkeley

Please Note: Note time and place of seminar

Ordered groups and n-dimensional dynamics

Series
School of Mathematics Colloquium
Time
Friday, December 6, 2019 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dale RolfsenUBC

A group is said to be torsion-free if it has no elements of finite order.  An example is the group, under composition, of self-homeomorphisms (continuous maps with continuous inverses) of the interval I = [0, 1] fixed on the boundary {0, 1}.  In fact this group has the stronger property of being left-orderable, meaning that the elements of the group can be ordered in a way that is nvariant under left-multiplication.  If one restricts to piecewise-linear (PL) homeomorphisms, there exists a two-sided (bi-)ordering, an even stronger property of groups.

I will discuss joint work with Danny Calegari concerning groups of homeomorphisms of the cube [0, 1]^n fixed on the boundary.  In the PL category, this group is left-orderable, but not bi-orderable, for all n>1.  Also I will report on recent work of James Hyde showing that left-orderability fails for n>1 in the topological category.  

Thresholds versus fractional expectation-thresholds

Series
Combinatorics Seminar
Time
Friday, December 6, 2019 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jinyoung ParkRutgers University

(This is a joint event of the Combinatorics Seminar Series and the ACO Student Seminar.)

In this talk we will prove a conjecture of Talagrand, which is a fractional version of the “expectation-threshold” conjecture of Kalai and Kahn. This easily implies various difficult results in probabilistic combinatorics, e.g. thresholds for perfect hypergraph matchings (Johansson-Kahn-Vu) and bounded-degree spanning trees (Montgomery). Our approach builds on recent breakthrough work of Alweiss, Lovett, Wu, and Zhang on the Erdos-Rado “Sunflower Conjecture.” 

This is joint work with Keith Frankston, Jeff Kahn, and Bhargav Narayanan.

Thresholds versus fractional expectation-thresholds

Series
ACO Student Seminar
Time
Friday, December 6, 2019 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jinyoung ParkRutgers University

Please Note: (This is a joint event of ACO Student Seminar and the Combinatorics Seminar Series)

In this talk we will prove a conjecture of Talagrand, which is a fractional version of the “expectation-threshold” conjecture of Kalai and Kahn. This easily implies various difficult results in probabilistic combinatorics, e.g. thresholds for perfect hypergraph matchings (Johansson-Kahn-Vu) and bounded-degree spanning trees (Montgomery). Our approach builds on recent breakthrough work of Alweiss, Lovett, Wu, and Zhang on the Erdős-Rado “Sunflower Conjecture.” 

This is joint work with Keith Frankston, Jeff Kahn, and Bhargav Narayanan.

An isoperimetric inequality for the Hamming cube and some consequences

Series
ACO Seminar
Time
Thursday, December 5, 2019 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jinyoung ParkRutgers University

I will introduce an isoperimetric inequality for the Hamming cube and some of its applications. The applications include a “stability” version of Harper’s edge-isoperimetric inequality, which was first proved by Friedgut, Kalai and Naor for half cubes, and later by Ellis for subsets of any size. Our inequality also plays a key role in a recent result on the asymptotic number of maximal independent sets in the cube. 

This is joint work with Jeff Kahn.

Geometry and analysis of degenerating Calabi-Yau manifolds

Series
Job Candidate Talk
Time
Thursday, December 5, 2019 - 12:15 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ruobing ZhangSUNY Stony Brook

This talk concerns a naturally occurring family of Calabi-Yau manifolds that degenerates in the sense of metric geometry, algebraic geometry and nonlinear PDE. A primary tool in analyzing their behavior is the recently developed regularity theory. We will give a precise description of arising singularities and explain possible generalizations. 

Inferring computation from structure in neuronal networks

Series
Job Candidate Talk
Time
Thursday, December 5, 2019 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Hannah ChoiUniversity of Washington

The complex connectivity structure unique to the brain network is believed to underlie its robust and efficient coding capability. Specifically, neuronal networks at multiple scales utilize their structural complexities to achieve different computational goals. In this talk, I will discuss functional implications that can be inferred from the architecture of brain networks.

The first part of the talk will focus on a generalized problem of linking structure and dynamics of the whole-brain network. By simulating large-scale brain dynamics using a data-driven network of phase oscillators, we show that complexities added to the spatially embedded brain connectome by idiosyncratic long-range connections, enable rapid transitions between local and global synchronizations. In addition to the spatial dependence, I will also discuss hierarchical structure of the brain network. Based on the data-driven layer-specific connectivity patterns, we developed an unsupervised method to find the hierarchical organization of the mouse cortical and thalamic network. The uncovered hierarchy provides insights into the direction of information flow in the mouse brain, which has been less well-defined compared to the primate brain.

Finally, I will discuss computational implications of the hierarchical organization of the brain network. I will focus on a specific type of computation – discrimination of partially occluded objects— carried out by a small cortical circuitry composed of an intermediate visual cortical area V4 and its efferent prefrontal cortex. I will explore how distinct feedforward and feedback signals promote robust encoding of visual stimuli by leveraging predictive coding, a Bayesian inference theory of cortical computation which has been proposed as a method to create efficient neural codes. We implement a predictive coding model of V4 and prefrontal cortex to investigate possible computational roles of feedback signals in the visual system and their potential significance in robust encoding of nosy visual stimuli.

In sum, our results reveal the close link between structural complexity and computational versatility found in brain networks, which may be useful for developing more efficient artificial neural networks and neuromorphic devices.

A new proof of the Caffarelli contraction theorem

Series
High Dimensional Seminar
Time
Wednesday, December 4, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Max FathiMathematics Institute, Toulouse, France

The Caffarelli contraction theorem states that the Brenier map sending the
Gaussian measure onto a uniformly log-concave probability measure is
lipschitz. In this talk, I will present a new proof, using entropic
regularization and a variational characterization of lipschitz transport
maps. Based on joint work with Nathael Gozlan and Maxime Prod'homme.

Branched covers and contact 3 manifolds

Series
Geometry Topology Student Seminar
Time
Wednesday, December 4, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Agniva RoyGeorgia Tech

Branched covers are a generalization of covering spaces, and give rise to interesting questions in smooth as well as contact topology. All 3 manifolds arise as branched coverings of the 3-sphere. The talk will involve a discussion of the proof of this fact due to Montesinos, and will explore the work done towards understanding which contact 3 manifolds arise as the branched cover of the standard tight 3 sphere, and how the branch set can be regulated.

Domino Tilings of the Chessboard: An Introduction to Sampling and Counting

Series
Undergraduate Seminar
Time
Monday, December 2, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Dana RandallGeorgia Tech

Domino tilings of finite grid regions have been studied in many contexts, revealing rich combinatorial structure.  They arise in applications spanning physics, computer science and probability theory and recreational mathematics.  We will look at questions such as counting and sampling from large combinatorial sets, such as the set of domino tilings, providing a small sample of some of the techniques that are used.  

 

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