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October 28, 2021 (Thursday), 2:00 pm

Dissertation Defense-Growth Of Dehn Twist and Pseudo-Anosov Conjugacy Classes in Teichmüller Space- Location: SC1312

Jiawei Han, Vanderbilt University- Zoom Not Available

Athreya, Bufetov, Eskin and Mirzakhani have shown the number of mapping class group lattice points intersecting a closed ball of radius $R$ in Teichmüller space is asymptotic to $e^{hR}$, where $h$ is the dimension of the Teichmüller space. In contrast, we first show the number of Dehn twist lattice points intersecting a closed ball of radius $R$ is coarsely asymptotic to $e^{hR/2}$. Moreover, we show the number of all multi-twists lattice points intersecting a closed ball of radius $R$ grows coarsely at least at the rate of $R e^{hR/2}$. Furthermore, we show for any pseudo-Anosov mapping class $f$, there exists a power $n$, such that the number of lattice points of the $f^n$ conjugacy class intersecting a closed ball of radius $R$ is coarsely asymptotic to $e^{hR/2}$. Finally, we could discuss a few open questions and a conjecture.

 

 

 

 

October 29, 2021 (Friday), 11:30 am

Subfactor Seminar

Irreducible inclusions of simple C*-algebras

Mikael Rordam, University of Copenhagen
Zoom ID 94393956397 Subfactor Seminar page for Zoom meeting information

There are several naturally occurring interesting examples of inclusions of simple C*-algebras with the property that all intermediate C*-algebras likewise are simple. By an analogy to von Neumann algebras, we refer to such inclusions as being C*-irreducible. We give an intrinsic characterization of C*-irreducible inclusions, and use this characterization to exhibit (and revisit) such inclusions, both known ones and new ones, arising from groups and dynamical systems. By a theorem of Popa, an inclusion of II_1-factors is C*-irreducible if and only if it is irreducible with finite Jones index. We explain how one can construct C*-irreducible inclusions from inductive limits. In a recent joint work with Echterhoff we consider when inclusions of the form $A^H \subseteq A \rtimes G$ are C*-irreducible, where G and H are groups acting on a C*-algebra A. Such inclusions in the setting of II_1 factors were considered by Bisch and Haagerup.

 

October 29, 2021 (Friday), 2:30 pm

PDE Seminar

PDE-Seminar- Generalized Price’s law on fractional-order asymptotically flat stationary spacetimes

Katrina Morgan, Northwestern University
PDE Seminar page for Zoom meeting information

Price’s law is a conjecture from the 70’s by physicist R. Price predicting that waves on the Schwarzschild spacetime decay pointwise at a rate of 1/t^3. The Schwarzschild geometry, which describes spacetime in the presence of a stationary black hole, is a long range perturbation of the flat Minkowski metric. On the other hand, we know that waves decay infinitely fast on Minkowski space as can be seen by sharp Huygens’ principle. In the current work we study decay rates of waves on stationary spacetimes which are short range perturbations of Minkowski space. In particular, the geometries considered have a prescribed rate at which they tend toward flat as the size of the spatial variables tends toward infinity. We describe the pointwise decay rate of waves in terms of this prescribed rate toward flatness. We are specifically interested in the case where the prescribed rate takes on non-integer values as the integer case was considered in previous work by M. The background geometries are allowed to exhibit weak trapping. This work shows it is the far away behavior of an asymptotically flat stationary spacetime which dictates the local decay rate of waves. This is joint work with Jared Wunsch.

November 3, 2021 (Wednesday), 4:10 pm

Computational Analysis Seminar

Computational Analysis- Incorporating Invariance to Reduce the Complexity of Parametric Models

Alex Cloninger, University of California – San Diego
Computational Analysis Seminar page for Zoom meeting information

Many scientific problems involve invariant structures, and learning functions that rely on a much lower dimensional set of features than the data itself.   Incorporating these invariances into a parametric model can significantly reduce the model complexity, and lead to a vast reduction in the number of labeled examples required to estimate the parameters.  We display this benefit in two settings.  The first setting concerns ReLU networks, and the size of networks and number of points required to learn certain functions and classification regions.  Here, we assume that the target function has built in invariances, namely that it only depends on the projection onto a very low dimensional, function defined manifold (with dimension possibly significantly smaller than even the intrinsic dimension of the data).  We use this manifold variant of a single or multi index model to establish network complexity and ERM rates that beat even the intrinsic dimension of the data.  We should note that the corollary of this result is developing intrinsic rates for a manifold plus noise data model without needing to assume the distribution of the noise decays exponentially.  The second setting for building invariances concerns linearized optimal transport (LOT), and using it to build supervised classifiers on distributions.  Here, we construct invariances and bound the error for deformations from various families of group actions, and show that LOT can learn a classifier on group orbits using a simple linear separator.   We demonstrate the benefit of this on MNIST by constructing robust classifiers with only a small number of labeled examples.  This talk covers joint work with Timo Klock and Caroline Moosmueller.

November 5, 2021 (Friday), 2:30 pm

PDE Seminar

PDE- Title: TBA

Junyan Zhang, Johns Hopkins University
PDE Seminar page for Zoom meeting information

 

 

November 5, 2021 (Friday), 4:10 pm

Subfactor Seminar

Subfactor Seminar- Title TBD

Changying Ding, Vanderbilt University
Zoom ID 94393956397 Subfactor Seminar page for Zoom meeting information

November 10, 2021 (Wednesday), 4:10 pm

Computational Analysis Seminar

Computational Analysis- Title TBD

Bernhard Bodmann, University of Houston
Computational Analysis Seminar page for Zoom meeting information

November 12, 2021 (Friday), 2:30 pm

PDE Seminar

PDE Seminar- Title- TBD

Federico Pasqualotto, Duke University
PDE Seminar

November 12, 2021 (Friday), 2:30 pm

PDE Seminar

PDE- Title- TBD

Federico Pasqualotto, Duke University
PDE Seminar page for Zoom meeting information

November 12, 2021 (Friday), 4:10 pm

Subfactor Seminar

Subfactor Seminar- Title TBD

Corey Jones, North Carolina State University
Zoom ID 94393956397 Subfactor Seminar page for Zoom meeting information

November 17, 2021 (Wednesday), 4:10 pm

Computational Analysis Seminar

Computational Analysis- Title- TBD

Yvonne Ou, University of Delaware
Computational Analysis Seminar page for Zoom meeting information

November 19, 2021 (Friday), 4:10 pm

Subfactor Seminar

Subfactor Seminar- Title- TBD

Sorin Popa, UCLA
Subfactor Seminar page for Zoom meeting information Zoom ID 94393956397

December 1, 2021 (Wednesday), 4:10 pm

Computational Analysis Seminar

Computational Analysis- Title TBD

Peter Hinow, University of Wisconsin, Milwaukee
Computational Analysis Seminar page for Zoom meeting information

December 3, 2021 (Friday), 2:30 pm

PDE Seminar

PDE- Title TBD

Ákos Nagy, UC Santa Barbara
PDE Seminar page for Zoom meeting information

December 3, 2021 (Friday), 4:10 pm

Subfactor Seminar

Subfactor Seminar- Title TBD

James Tener, ANU Mathematical Sciences Institute
Zoom ID 94393956397 Subfactor Seminar page for Zoom meeting information