Seminar Calendar
for events the day of Thursday, February 9, 2017.

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Thursday, February 9, 2017

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, February 9, 2017
Submitted by sahlgren.
Matthias Strauch (Indiana University Bloomington)
Coverings of the p-adic upper half plane and arithmetic differential operators
Abstract: The p-adic upper half plane comes equipped with a remarkable tower of GL(2)-equivariant etale covering spaces, as was shown by Drinfeld. It has been an open question for some time whether the spaces of global sections of the structure sheaf on such coverings provide admissible locally analytic representations. Using global methods and the p-adic Langlands correspondence for GL(2,Qp), this is now known to be the case by the work of Dospinescu and Le Bras. For the first layer of this tower Teitelbaum exhibited a nice formal model which we use to provide a local proof for the admissibility of the representation (when the base field is any finite extension of Qp). The other key ingredients are suitably defined sheaves of arithmetic differential operators and D-affinity results for formal models of the rigid analytic projective line, generalizing those of Christine Huyghe. This is joint work with Deepam Patel and Tobias Schmidt.

Math-Physics Seminar
12:30 pm   in 464 Loomis Laboratory,  Thursday, February 9, 2017
Submitted by katz.
Mboyo Esole (Northeastern Math)
Anomaly free SO(3), SO(5), and SO(6) gauge theories from F Theory
Abstract: Orthogonal groups in F Theory are delicate to define as they require a condition on the Mordell-Weil group of the generic elliptic fiber to distinguish them from spin groups. Moreover, the orthogonal groups discussed in the literature are SO (7+k) with k>0. In this talk, I will discuss the explicit construction of lower rank orthogonal groups in F Theory, classify their singular fibers and matter content in 4, 5, and 6 dimensional spacetimes. I will also present the details of their uplift from 5 to 6 dimensions, the cancellations of 6 dimensional anomalies and the structure of the Coulomb phases of the five dimensional theory. All this will be presented as an exercise in intersection theory using a new pushforward theorem for Chow rings of blowups.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, February 9, 2017
Submitted by tumanov.
Ben Wallis (Northern Illinois University)
Garling sequence spaces
Abstract: By generalizing a construction of Garling, for each $1\leqslant p<\infty$ and each normalized, nonincreasing sequence of positive numbers $w\in c_0\setminus\ell_1$ we exhibit an $\ell_p$-saturated, complementably homogeneous Banach space $g(w,p)$ related to the Lorentz sequence space $d(w,p)$. Using methods originally developed for studying $d(w,p)$, we show that $g(w,p)$ admits a unique (up to equivalence) subsymmetric basis, although when the weight $w$ satisfies a certain bi-regularity condition, it does not admit a symmetric basis. We then discuss some additional properties of $g(w,p)$ related to uniform convexity and superreflexivity. Joint work with Fernando Albiac and J. L. Ansorena.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, February 9, 2017
Submitted by kapovich.
Mboyo Esole (Northeastern Math)
Tales of Elliptic fibrations
Abstract: Elliptic curves have been part of mathematics since ancient Greece and beyond. When an elliptic curve moves over a variety, it draws a fibration called a genus one fibration. The cases of surfaces have been explored by Kodaira, Neron, and others in the early 1960s. During the second string revolution, elliptic fibrations have played a central role in describing non-perturbative effects in string theory and M-theory. Ever since, ideas from physics have inspired new points of view on elliptic fibrations, providing a rich set of ideas to explore their geometry using tools from representation theory, hyperplane arrangements, intersection theory, and birational geometry. In this colloquium, I will review these ideas and present new results.