# Math Calendar

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A live feed of seminars and special events in the upcoming week.

December 1st, 2015 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Generalized Frobenius partitions and Jacobi forms
Speaker: Larry Rolen, PSU
Location: MB106

In a 1984 memoir, Andrews defined the notion of a generalized Frobenius partition. Since then, many authors have considered explicit formulas and congruences for functions counting these objects. Here, in joint work with Kathrin Bringmann and Mike Woodbury, I will show how interpreting these functions in the context of Jacobi forms and theta decompositions gives a natural interpretation of the counting functions for generalized Frobenius partitions into $k$ colors in terms of character formulas of Kac and Wakimoto, and how the structure of theta decompositions can be used to give inductive formulas for the generating functions.

December 1st, 2015 (01:30pm - 02:20pm)
Seminar: Theoretical Biology Seminar
Title: Modeling HIV latency reversing agents and its implications for clinical trial design
Speaker: Ruian Ke, North Carolina State University
(Host: Jessica Conway)
Location: MB106

A major barrier to cure HIV infection is the existence of a population of long lived latently infected cells, i.e. the HIV latent reservoir. Recent efforts have focused on developing latency reversing agents (LRAs) to activate HIV expression in latently infected cells in order to purge the HIV latent reservoir. However, it is not clear to what extent LRAs impact the latency reversing process and which steps in the process determine the rate of reservoir reduction. Furthermore, accurately measuring the size of the reservoir experimentally has been challenging. All these issues make evaluating the efficacy of candidate LRAs and predicting treatment outcomes difficult. To address these issues, we developed a series of mathematical models to describe the dynamics of latently infected cells under LRA treatment. In the first part of the talk, I will present our work on understanding the impact of one of the first LRAs, vorinostat. By fitting viral dynamic models to clinical data, we show that vorinostat induces both transient and delayed HIV transcriptional activation in vivo . However, killing of latently infected cells in treated patients is minimal. In the second part of the talk, I will discuss a stochastic model that incorporates both HIV activation process in vivo and clinical sampling procedures in a probabilistic framework. We identify key parameters that determine the rate of latent reservoir reduction, and using information theory, we evaluate the accuracy in estimating these parameters using data collected from three commonly used experimental assays. To conclude, this framework provides a useful tool for designing future clinical trials and experiments to evaluate the efficacy of candidate LRAs and predict long-term treatment outcomes.

December 1st, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Algebraic Families of Harish-Chandra pairs and their modules II
Speaker: Eyal Subag, Penn State
Location: MB106

In my talk I will try to convince you that Lie groups come in natural algebraic families. A construction of such families that relates different real forms of GL(n,C), and SL(n,C) will be given. Moreover, we shall see that we can naturally associate families of Harish-Chandra pairs to these families of groups. For the family that goes through SU(2), SU(1,1), and their Cartan motion group, a classification of generically irreducible Harish Chandra modules will be given. As an application, a formulation of the Mackey bijection between the duals of SU(1,1) and its Cartan motion group in terms of families of Harish Chandra modules will be presented. The talk is based on a joint work with Joseph Bernstein and Nigel Higson.

December 1st, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Hausdorff Dimension, Irrationality Exponents and Their Effectivization
Speaker: Jan Reimann, Penn State
Location: MB315

We generalize the classical theorem by Jarnik and Besicovitch on the irrationality exponents of real numbers and Hausdorff dimension. Let a be any real number greater than or equal to 2 and let b be any non-negative real less than or equal to 2/a. We show that there is a Cantor-like set with Hausdorff dimension equal to b such that, with respect to its uniform measure, almost all real numbers have irrationality exponent equal to a. We give an analogous result relating the irrationality exponent and the Hausdorff dimension of individual real numbers. We prove that there is a Cantor-like set such that, with respect to its uniform measure, almost all reals in the set have effective Hausdorff dimension equal to b and irrationality exponent equal to a. This is joint work with V. Becher and T. Slaman.

December 1st, 2015 (02:30pm - 03:29pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Non hyperbolic dynamics and non-hyperbolic measures.
Speaker: Christian Bonatti, University of Dijon
Location: MB114

Hyperbolicity provides a simple understanding of chaotic dynamics. In some sense, hyperbolic dynamics are the most complicated dynamics for which one can give a complete topological description. An even more precise description of the dynamics of hyperbolic systems can be obtained through ergodic theory. However, hyperbolic systems are far from being all chaotic systems: there are numerous robustly non-hyperbolic systems. I will review several results and mechanisms showing that the existence of non-hyperbolic measures can be robust. In fact, the robust existence of non hyperbolic measure may be the most common situation in the non-hyperbolic world. I will review several results and mechanisms showing that the existence of non-hyperbolic measures can be robust. In fact, the robust existence of non hyperbolic measure may be the most common situation in the non-hyperbolic world.

December 1st, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Partially hyperbolic diffeomorphisms of 3 manifolds I. ATTENTION: THIS TALK WILL START AT 3:45pm
Speaker: Christian Bonatti, University of Dijon
Location: MB114

For decades, the only known examples of partially hyperbolic diffeoomorphisms on 3-manifolds were "center-leaf conjugated", up to taking lift to finite covers and finite powers, to three simple models: -- time one map of Anosov flows -- Anosov diffeomorphisms on T3 with 3 real distinct eigenvalues -- a skew product of an Anosov diffeomorphism of T2 by circle diffeomorphism. Recently many new examples appear, still very related with the models but not isotopic to them: -- (non transitive) partially hyperbolic diffeomorphisms on T3 whose center bundle is robustly not tangent to any foliation. -- (transitive and not transitive) partially hyperbolic diffeomorphisms on manifolds supporting an Anosov flow, which are not isotopic to identity. I will present these new examples. The first of them is already written and it opened the door to building many more: I will also present many examples that are still work in progress.

December 2nd, 2015 (12:00pm - 01:30pm)
Seminar: Geometry Luncheon Seminar
Title: TBA
Speaker: Carina Curto, Penn State
Location: MB114
December 3rd, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Convolution algebras and group representations I
Speaker: Nigel Higson, PSU
Location: MB106
December 3rd, 2015 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Faculty Meeting
Speaker: Faculty Meeting
Location: MB114
December 7th, 2015 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Flexibility of topological and metric entropies for surfaces of negative curvature.
Speaker: Alena Erchenko, Penn State
Location: MB114

We consider a smooth closed surface $M$ of fixed genus $\geqslant 2$ and fixed volume with a Riemannian metric $g$ of negative curvature. A. Katok has shown that the topological entropy of geodesic flow for $g$ is greater than or equal to the topological entropy for the metric of constant negative curvature on $M$ which is greater than or equal to the metric entropy with respect to the Liouville measure of geodesic flow for $g$. Equality holds only in the case of constant negative curvature. It turns out that this is the only restriction on pairs of values of topological and metric entropies. We will discuss several examples with particular distributions of curvature.

December 8th, 2015 (01:30pm - 02:20pm)
Seminar: Theoretical Biology Seminar
Title: Intra-individual evolution of the T cell repertoire
Speaker: Philip Johnson, University of Maryland, College Park
(Host: Jessica Conway)
Location: MB106

The vertebrate T cell adaptive immune response has the challenging task of recognizing any possible pathogen while never attacking "self." Evolution's solution to this challenge has been to generate a repertoire of T cells within a single individual via a process of recombination and intra-individual selection that creates a vast diversity of distinct T cell receptors (TCRs). High throughput sequencing enables serial, deep sampling of this repertoire and thus allows us to address long standing questions regarding how the repertoire is formed and shaped over the lifetime of the individual. These data have required the development of methods to account for sequencing error in pooled samples of mixed frequencies and to account for variation among biological replicates. I will present these methods along with data from experimental collaborators as I investigate the question of "Why do we see public T cell responses with the the same TCRs in different individuals?"

December 8th, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: TBA
Speaker: Zvi Rosen, Penn State
Location: MB106
December 8th, 2015 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Triviality and lowness for K-reducibility and related reducibilities
Speaker: William C. Calhoun, Bloomsburg University
Location: MB315

A set of natural numbers A is K-trivial if K(A|n) <= K(n)+O(1) for all natural numbers n (where A|n is A restricted to n and K is prefix-free Kolmogorov complexity). The set A is low for K if K^{A}(y)=K(y)+O(1) for all binary strings y. These definitions seem quite different. K-triviality indicates that initial segments of A have the lowest possible complexity, while lowness for K indicates that A is too weak as an oracle to reduce the complexity of any string. The remarkable equivalence of the two definitions was shown in [2]. Replacing prefix-free complexity by monotone complexity in the definition of K-trivial, we obtain the Km-trivial sets. Every K-trivial set is Km-trivial and all Turing degrees >= 0' contain a Km-trivial set [1]. Yet, not every Turing degree contains a Km-trivial set. We obtain a superset of the Km-trivial sets by defining A to be almost trivial if there is a real number a such that K(A|n) <= aK(n) +O(1). Every Km-trivial set is almost trivial. However, the Turing degree of a computably dominated ML-random cannot contain any almost trivial set. An interesting question is to determine which Turing degrees contain Km-trivial sets (or almost trivial sets). Recently, this question has been considered for minimal Turing degrees. We also consider lowness for monotone and a priory complexity.

[1] Calhoun, W.C.: Triviality and minimality in the degrees of monotone complexity, Journal of Logic and Computation 22, 197-206 (2012).

[2] Nies, Andre: Lowness properties and randomness, Advances in Mathematics 197, 274-305 (2005).

December 8th, 2015 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Partially hyperbolic diffeomorphisms of 3 manifolds. II
Speaker: Christian Bonatti, University of Dijon
Location: MB114

For decades, the only known examples of partially hyperbolic diffeoomorphisms on 3-manifolds were "center-leaf conjugated", up to taking lift to finite covers and finite powers, to three simple models: -- time one map of Anosov flows -- Anosov diffeomorphisms on T3 with 3 real distinct eigenvalues -- a skew product of an Anosov diffeomorphism of T2 by circle diffeomorphism. Recently many new examples appear, still very related with the models but not isotopic to them: -- (non transitive) partially hyperbolic diffeomorphisms on T3 whose center bundle is robustly not tangent to any foliation. -- (transitive and not transitive) partially hyperbolic diffeomorphisms on manifolds supporting an Anosov flow, which are not isotopic to identity. I will present these new examples. The first of them is already written and it opened the door to building many more: I will also present many examples that are still work in progress.

December 9th, 2015 (12:00pm - 01:30pm)
Seminar: Geometry Luncheon Seminar
Title: TBA
Speaker: Jeffrey Case, Penn State
Location: MB114
December 10th, 2015 (10:30am - 05:00pm)
Seminar: Department of Mathematics Colloquium
Title: Staff Appreciation Tea
Speaker: Staff Appreciation Tea
Location: MB114
December 10th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Algebra and Number Theory Seminar
Speaker: Will be on Friday, 11:15, room MB114, None
Location: MB106

Valentin Blomer will speak on Friday

December 10th, 2015 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Convolution algebras and group representations II
Speaker: Nigel Higson, PSU
Location: MB106
December 10th, 2015 (05:10pm - 07:10pm)
Seminar: Ph.D. Oral Comprehensive Examination
Title: "Thermodynamics of some non-uniformly hyperbolic attractors"
Speaker: Agnieszka Zelerowicz-Adviser, Yakov Pesin, Penn State
Location: MB106
December 11th, 2015 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: On a certain senary cubic form
Speaker: Valentin Blomer, Institute for Advanced Study and University of Goettingen
Location: MB114

We establish an asymptotic formula (with power saving error term) for the number of rational points of bounded height for a certain cubic fourfold, thereby proving a strong form of Manin's conjecture for this case by a variety techniques from analytic number theory, combinatorics and arithmetic geometry.

December 15th, 2015 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Localization and the canonical commutation relations
Speaker: Patrick Moylan, Penn State
Location: MB106
Abstract: http://www.personal.psu.edu/ndh2/MoylanGapAbstract.pdf