## Chromatic homotopy theory

Irina Bobkova

Member, School of Mathematics

September 26, 2017

Irina Bobkova

Member, School of Mathematics

September 26, 2017

Nathaniel Bottman

Member, School of Mathematics

September 26, 2017

Guillaume Brunerie

Member, School of Mathematics

September 26, 2017

Ashay Burungale

Member, School of Mathematics

September 26, 2017

Eshan Chattopadhyay

Member, School of Mathematics

September 26, 2017

Gao Chen

Member, School of Mathematics

September 26, 2017

I will start from a simple statement: the radius of a sphere determines the shape of it. This simple statement has been generalized to the study of Riemann surfaces, K3 surfaces, Hyperkähler manifolds and other important objects. Recently, the conjecture about the generalization to the subject of special holonomy has drawn many attentions.

Toniann Pitassi

University of Toronto; Visiting Professor, School of Mathematics

September 26, 2017

Communication complexity studies the minimal amount of information two parties need to exchange to compute a joint function of their inputs. Results, especially lower bounds in this basic model found applications in many other areas of computer science.

Umesh Vazirani

University of California, Berkeley

September 18, 2017

Alex Smith

Harvard University

September 14, 2017

Take \(E/Q\) to be an elliptic curve with full rational 2-torsion (satisfying some extra technical assumptions). In this talk, we will show that 100% of the quadratic twists of \(E\) have rank less than two, thus proving that the BSD conjecture implies Goldfeld's conjecture in these families. To do this, we will extend Kane's distributional results on the 2-Selmer groups in these families to \(2^k\)-Selmer groups for any \(k > 1\).

Manuel Rivera

University of Miami

May 11, 2017

The string topology coproduct is an intersection type operation, originally described by Goresky-Hingston and Sullivan, which considers transverse self-intersections on chains of loops in a smooth manifold and splits loops at these intersection points. The geometric chain level construction of string topology operations involves deforming chains to achieve certain transversality conditions and these deformations introduce higher homotopy terms for algebraic compatibilities and properties.