Events

Rahim Moosa, University of Waterloo

Definable groups in CCM

I will survey what is known about the structure of definable groups in both the standard and nonstandard models of CCM.

MC 5479

Faisal Romshoo, University of Waterloo

Deformations of calibrations

We will look at a criterion for unobstructedness for calibrations and see when the corresponding moduli spacesform smooth manifolds, following the approach by Goto in https://arxiv.org/abs/math/0112197

MC 5403

Evan Sundbo, University of Waterloo

Broken Toric Varieties and Balloon Animal Maps

We will see the definition and some examples of broken toric varieties and balloon animal maps between them. After an overview of some of the many different areas in which they appear, we look at how their geometry can be studied via complexes of sheaves on an associated complex of polytopes. This yields results such as a version of the Decomposition Theorem and some explicit formulas for dimensions of rational cohomology groups of broken toric varieties.

MC 5417

Open Mic

Come listen to or contribute a minitalk (no longer than 15 minutes). Anything (as long as it vaguely relates tomathematics and is reasonably accessible) goes!

MC 5479

(Refreshments will start at 16:30)

Matthew Young, Rutgers University

The shifted convolution problem for Siegel modular forms

The shifted convolution problem for Fourier coefficients of cusp forms has seen a lot of attention due to applications towards moments of L-functions and the subconvexity problem. However, the problem for higher rank automorphic forms (beyond GL_2) has been a notorious bottleneck towards progress on the sixth moment of the Riemann zeta function. In this talk, I will discuss recent progress on the problem for Siegel cusp forms on Sp_4. This is joint work with Wing Hong (Joseph) Leung.

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Damaris Schindler, University of Göttingen

Density of rational points near manifolds

Given a bounded submanifold M in R^n, how many rational points with common bounded denominator are there in a small thickening of M? How does this counting function behave if we let the size of the denominator go to infinity? The study of the density of rational points near manifolds has seen significant progress in the last couple of years. In this talk I will explain why we might be interested in this question, focusing on applications in Diophantine approximation and the (quantitative) arithmetic of projective varieties.

MC 5403

Damaris Schindler, University of Göttingen

Quantitative weak approximation and quantitative strong approximation for certain quadratic forms

In this talk we discuss recent results on optimal quantitative weak approximation for certain projective quadrics over the rational numbers as well as quantitative results on strong approximation for quaternary quadratic forms over the integers. We will also discuss results on the growth of integral points on the three-dimensional punctured affine cone and strong approximation with Brauer-Manin obstruction for this quasi-affine variety. This is joint work with Zhizhong Huang and Alec Shute.

MC 5479