# Calendar

## Yesterday

## Hyperbolic polygons

Abstract: In this talk, I will talk about trigonometry of hyperbolic polygons and formulas for computing areas such as a law of sines. I will use these to get information about tiling of hyperbolic plane which gives arise to Fenchel-Nielsen coordinates for the moduli space for Riemann surfaces. No prior knowledge in Riemannian geometry will be assumed. Refreshments will be served as usual.### Mathematical Physics Seminar, Lara Anderson, Virginia Tech, REC 317

Thursday, Apr 19 1:30 pm - 2:20 pm

## Calabi-Yau fibrations in string theory

I will describe recent efforts to systematically study fibrations within Calabi-Yau threefolds and their consequences for string compactifications. This includes a recent enumeration of all genus one fibrations in class of 7890 Calabi-Yau manifiolds defined as complete intersections in products of projective spaces (so-called CICY threefolds). This survey is a complete classification that depends only on topology and improves upon past approaches that probed only a particular algebraic form of the manifold. I will also describe K3-fibrations and so-called “nested" fibration structures (for example, K3 fibrations in which the generic fiber can in turn can be elliptically fibered in many distinct ways).### Automorphic Forms and Representation Theory Seminar, Dr. Cris Negron, MIT, UNIV 317

Thursday, Apr 19 1:30 pm - 2:20 pm

## Cohomology for Drinfeld doubles of finite group scheme

Abstract: In the mid 2000's Etingof and Ostrik conjectured that the cohomology $H^\ast(A,\mathbb{F})$ of any finite dimensional Hopf algebra $A$ over an arbitrary field $\mathbb{F}$ is itself a finitely generated algebra, under the standard (Yoneda) product. This conjecture was motivated, in part, by fantastic work of Friedlander and Suslin from the 90's, in which they showed that any finite group scheme in characteristic $p$ has finitely generated cohomology. I will discuss joint work with E. Friedlander, where we return to the finite characteristic setting to provide a strong analysis of cohomology for so-called Drinfeld doubles of finite group schemes. I will discuss the central role such doubles play in the more general theory of finite tensor categories, and explain how the cohomology of such doubles can be understood via “classical" data.## Next Week

Title: The Effective Reproduction Number for a Class of Mixing Matrices in Meta-Population Models in Epidemiology

### Automorphic Forms and Representation Theory Seminar, Prof. Helene Esnault, Freie Universität Berlin, REC 308

Monday, Apr 23 3:00 pm - 4:00 pm

Title of Talk: Companions

Abstract: We give some background on companions (a notion due to Deligne) for l-adic sheaves, and if time permits, for F-overconvergent isocrystals as well. (On the latter: joint work with Tomoyuki Abe)

### Student Commutative Algebra Seminar, Mr. Cheng Meng, Purdue University, REC 313

Monday, Apr 23 3:30 pm - 4:30 pm

## Monomial Resolutions

### CCAM Seminar, Dr. Andrew Hill, Centers for Disease Control and Prevention, REC 308

Monday, Apr 23 4:30 pm - 5:30 pm

## Striving for Realism in Mathematical Models of Infectious Disease: Two Cautionary Tales

The appropriate development of a mathematical model of infectious disease transmission begins with understanding the problem that is being represented. Thus, building a good model for use in public health policy and decision making generally requires consultation with subject matter experts. Examples of relevant factors that may be crucial to capture are demographic trends, contact patterns describing how individuals mix with each other, and underlying epidemiologic processes specific to the disease in question. In this talk, I look at two separate examples to illustrate what can go wrong if realistic assumptions are ignored. The first considers heterogeneity in mixing among sub-populations and demonstrates that this should be considered when evaluating public health interventions to prevent or control infectious disease outbreaks. Neglecting to do so can lead to under-estimation of reproduction numbers and control efforts. The second looks at the published modeling literature for tuberculosis and examines how progression from latent infection to disease has been modeled, and how closely different approaches taken agree with empirical evidence from epidemiologic and clinical studies. Given the long latency periods of tuberculosis infection, models which fail to replicate progression dynamics and latent period distributions may produce unreliable projections and run the risk of misinforming future policy.## A Functorial Approach to Groupoid Modeling of C*-algebras

Abstract: In joint works with Magdalena Georgescu and Atish Mitra, we have devised a way to do categorical modeling of c*-algebras using groupoids. Specifically, we have found morphisms of groupoids with Haar systems of measures that induce morphisms of maximal groupoid c*-algebras; moreover, our association of groupoid to maximal groupoid c*-algebra and our morphisms of groupoids to their induced morphisms is functorial and generalizes the Gelfand duality functor for spaces. We use this to construct explicit examples of lots of c*-algebras including the Jiang-Su and Razak Jacelon algebras. If there is time, I will also talk about our current project on finding an inverse functor from certain pairs of c*-algebras to groupoids.

### Department Colloquium, Prof. Helene Esnault, Freie Universitat Berlin, MATH 175

Tuesday, Apr 24 3:30 pm - 4:20 pm

## Rigidity and integrality

Abstract: We explain the general p-curvature conjecture, Simpson's geometricity conjecture and his integrality conjecture for irreducible rigid connections with finite determinant and quasi-unipotent monodromies at infinity. We give a sense of what is behind the proof of the integrality on cohomologically rigid connections. (Joint work with Michael Groechenig)### Algebraic Geometry Seminar, Prof. Helene Esnault, Freie Universität Berlin, MATH 731

Wednesday, Apr 25 3:25 pm - 4:25 pm

**Rigidity and F-isocrystals. **

Abstract: We explain that rigid connections yields F-overconvergent isocrystals (in the projective case) and discuss a few points concerning the p-curvature conjecture. (Joint work with Michael Groechenig)

### Mathematical Physics Seminar, Rinat Kedem, U. of Illinois, Urbana-Champaign, REC 317

Thursday, Apr 26 1:30 pm - 2:20 pm

## Q-systems: Discrete integrability and cluster algebras

I’ll introduce a family of remarkable recursion relations, originally found in the context of the Bethe ansatz of generalized Heisenberg modules and quantum groups. I will reconsider this system as a discrete integrable system in its own right, and show some of the remarkable properties it and its quantization, via a cluster algebra formulation, exhibit. This will be a basic talk with no prior knowledge of any of the above mentioned topics assumed, with the purpose of introducing some of these structures and showing why they might be useful in mathematical physics.### Automorphic Forms and Representation Theory Seminar, Dr. Fan Gao (Purdue University), UNIV 317

Thursday, Apr 26 1:30 pm - 2:20 pm