My goal for the talk is to give a "from the ground-up" introduction to symplectic topology. We will cover the Darboux lemma, pseudo-holomorphic curves, Gromov-Witten invariants, quantum cohomology and Floer cohomology.

Aden Forrow
Optimal transport and cell differentiation

Abstract
Optimal transport is a rich theory for comparing distributions, with both deep mathematics and application ranging from 18th century fortification planning to computer graphics. I will tie its mathematical story to a biological one, on the differentiation of cells from pluripotency to specialized functional types. First the mathematics can support the biology: optimal transport is an apt tool for linking experimental samples across a developmental time course. Then the biology can inspire new mathematics: based on the branching structure expected in differentiation pathways, we can find a regularization method that dramatically improves the statistical performance of optimal transport.

Paul Ziegler
Geometry and Arithmetic

Abstract
For a family of polynomials in several variables with integral coefficients, the Weil conjectures give a surprising relationship between the geometry of the complex-valued roots of these polynomials and the number of roots of these polynomials "modulo p". I will give an introduction to this circle of results and try to explain how they are used in modern research.
 

Valérie Voorsluijs
Deterministic limit of intracellular calcium spikes
Abstract: In non-excitable cells, global calcium spikes emerge from the collective dynamics of clusters of calcium channels that are coupled by diffusion. Current modeling approaches have opposed stochastic descriptions of these systems to purely deterministic models, while both paradoxically appear compatible with experimental data. Combining fully stochastic simulations and mean-field analyses, we demonstrate that these two approaches can be reconciled. Our fully stochastic model generates spike sequences that can be seen as noise-perturbed oscillations of deterministic origin while displaying statistical properties in agreement with experimental data. These underlying deterministic oscillations arise from a phenomenological spike nucleation mechanism.

Matthias Nagel
Knots in dimensions three and four
Abstract: Knot theory studies the various embeddings of a circle into three-dimensional space. I will describe an equivalence relation on knots, called "concordance", which takes the fourth dimension into account. The study of concordance is intimately related with many problems at the heart of the topology of four-manifolds, such as the difference between the smooth and the topological category, and I will discuss results that illuminate this relation.

What is the point of giving a talk?  What is the point of going to a talk?  In this presentation, which is intended to have a lot of audience participation, I would like to explore how one should prepare talks for different audiences and different occasions, and what one should try to get out of going to a talk.

Six-dimensional theories provide a unification of four-dimensional theories via dimensional reduction  together with access to some of the novel features arising from M-theory.  Ambitwistor strings directly generate S-matrices for massless theories in terms of formulae that localize on the solutions to the scattering equations; algebraic equations that determine n points on the Riemann sphere from n massless momenta.  These are sufficient to provide compact formulae for tree-level S-matrices for bosonic theories. This talk introduces their extension to the polarized scattering equations which arise from twistorial versions on ambitwistor-strings.  These lead to simple explicit formulae for superamplitudes in 6D for super Yang-Mills, supergravity, D5 and M5 branes and massive superamplitudes in 4D.  The framework extends also to 10 and 11 dimensions.  This is based on joint work with Yvonne Geyer, arxiv:1812.05548 and 1901.00134. 

After a brief introduction to the theory of transcendental numbers, I will discuss Nesterenko's 1996 celebrated theorem on the algebraic independence of values of Eisenstein series, and some related open problems. This motivates the second part of the talk, in which I will report on a recent geometric generalization of Nesterenko's method.