## ABEL Prize Reception in Honor of Karen Uhlenbeck

Various Speakers

March 19, 2019

Toniann Pitassi

University of Toronto; Visiting Professor, School of Mathematics

March 19, 2019

I will give a tour of some of the key concepts and ideas in proof complexity. First, I will define all standard propositional proof systems using the sequent calculus which gives rise to a clean characterization of proofs as computationally limited two-player games. I will also define algebraic and semi-algebraic systems (SOS, IPS, Polynomial Calculus).

Matthew Gursky

University of Notre Dame

March 19, 2019

In this talk I want to discuss two related questions about

Xin Zhou

University of California, Santa Barbara; Member, School of Mathematics

March 19, 2019

I will present a proof with some substantial details of the Multiplicity One Conjecture in Min-max theory, raised by Marques and Neves. It says that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, Marques-Neves are all two-sided and have multiplicity one.

Imre Barany

Renyi Institute, Hungary and UCL, London

March 18, 2019

We show that, as a consequence of a remarkable new result of

Attila P\'or on universal Tverberg partitions, any large-enough set

$P$ of points in $\Re^d$ has a $(d+2)$-sized subset whose Radon point

has half-space depth at least $c_d \cdot |P|$, where $c_d \in (0, 1)$

depends only on $d$. We then give an application of this result to

computing weak $\eps$-nets by random sampling. Joint work with Nabil

Mustafa.

Barney Bramham

Ruhr University Bochum; von Neumann Fellow, School of Mathematics

March 18, 2019

Joel Fish

University of Massachusetts Boston

March 18, 2019

I will discuss some current joint work with Helmut Hofer, in which we define and establish properties of a new class of pseudoholomorhic curves (feral J-curves) to study certain divergence free flows in dimension three. In particular, we show that if H is a smooth, proper, Hamiltonian on R^4, then no non-empty regular energy level of H is minimal. That is, the flow of the associated Hamiltonian vector field has a trajectory which is not dense.

Ilya Kachkovskiy

Michigan State University

March 15, 2019

We consider a system of two interacting one-dimensional quasiperiodic particles as an operator on $\ell^2(\mathbb Z^2)$. The fact that particle frequencies are identical, implies a new effect compared to generic 2D potentials: the presence of large coupling localization depends on symmetries of the single-particle potential.

Alison Locke Perchuk

March 15, 2019

Yiannis Sakellaridis

Rutgers University

March 14, 2019

The thesis of Akshay Venkatesh obtains a ``Beyond Endoscopy'' proof of stable functorial transfer from tori to ${\rm SL}(2)$, by means of the Kuznetsov formula. In this talk, I will show that there is a local statement that underlies this work; namely, there is a local transfer operator taking orbital measures for the Kuznetsov formula to test measures on the torus. The global comparison of trace formulas is then obtained as a Poisson summation formula for this transfer operator.