ENG 
ESP MCA Prize Lectures
These lectures will be accessible live only to registered participants via Zoom. You can find the Zoom link to join on our forum.
Tuesday, July 20, 12:15 ~ 13:15 UTC-3
Flexibility in contact geometry
Emmy Murphy
Princeton, USA - This email address is being protected from spambots. You need JavaScript enabled to view it.
We discuss a number of results covering the past ten years of flexibility in symplectic and contact geometry. This typically takes the form of difficult geometric questions being reduced to topological classifications under the hypothesis of certain model neighborhoods.
Wednesday, July 21, 12:15 ~ 13:15 UTC-3
Random surfaces of large genus
Alex Wright
University of Michigan, United States - This email address is being protected from spambots. You need JavaScript enabled to view it.
I will survey different models of random hyperbolic surfaces of large genus, the analogies with random graphs that guides their study, and some of what is known. This will include my recent joint work with Mike Lipnowski (arXiv:2103.07496) that uses the Selberg trace formula and results of Mirzakhani to show the first eigenvalue of the Laplacian is typically large.
Joint work with Mike Lipnowski (University of McGill, Canada).
Thursday, July 22, 12:15 ~ 13:15 UTC-3
The KPZ fixed point
Daniel Remenik
Universidad de Chile, Chile - This email address is being protected from spambots. You need JavaScript enabled to view it.
The KPZ universality class is a broad collection of probabilistic models including one-dimensional random growth, directed polymers and particle systems. The class is characterized by an unusual and very rich fluctuation behavior, with asymptotic distributions which for some special choices of initial conditions are connected to random matrix theory. The KPZ fixed point is a special, scaling invariant Markov process which arises as the universal scaling limit of all models in the class, and contains all of its fluctuation behavior. In this talk I'm going to introduce this object and describe how it is obtained from certain special models in the class. I will then explain how the KPZ fixed point can be interpreted as a stochastic integrable system and how this leads to a connection with a famous completely integrable dispersive PDE, the Kadomtsev-Petviashvili equation.
Joint work with Konstantin Matetski (Columbia U.) and Jeremy Quastel (U. of Toronto).
Friday, July 23, 12:15 ~ 13:15 UTC-3
Pontryagin-Thom for orbifold bordism
John Pardon
Princeton University, USA - This email address is being protected from spambots. You need JavaScript enabled to view it.
The classical Pontryagin-Thom isomorphism equates manifold bordism groups with corresponding stable homotopy groups. Extensions of the Pontryagin-Thom isomorphism to equivariant bordism groups have been known classically due to Conner-Floyd, Wasserman, tom Dieck, Brocker-Hook, and more recently Schwede. I will discuss work which establishes a Pontryagin-Thom isomorphism for orbispaces (an orbispace is a "space" which is locally modelled on Y/G for Y a space and G a finite group; examples of orbispaces include orbifolds and moduli spaces of pseudo-holomorphic curves). A key step will be to implement Spanier-Whitehead duality in a certain stable homotopy category of orbispaces.