Upcoming Seminars & Events

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September 14, 2016
4:30pm - 5:30pm
The sphere packing problem in dimensions 8 and 24.

The sphere packing problem is to find an arrangement of non-overlapping unit spheres in the $d$-dimensional Euclidean space in which the spheres fill as large a proportion of the space as possible. In this talk we will present a solution of the sphere packing problem in dimensions 8 and 24. In 2003 N. Elkies and H. Cohn  proved that the existence of a real function satisfying certain constrains leads to an upper bound for the sphere packing constant. Using this method they obtained almost sharp estimates in dimensions 8 and 24. We will show that functions providing exact bounds can be constructed explicitly as certain integral transforms of modular forms. Therefore, the sphere packing problem in dimensions 8 and 24 is solved by a linear programming method.

Speaker: Maryna Viazovska, Humboldt University
Location:
Fine Hall 314
September 21, 2016
3:00pm - 4:00pm
TBD - Stephen McKeown
Speaker: Stephen McKeown, Princeton University
Location:
Fine Hall 314
September 27, 2016
4:30pm - 5:30pm
TBD - Eliran Subag
Speaker: Eliran Subag, Weizmann Institute
Location:
Jadwin Hall 343
September 28, 2016
3:00pm - 4:00pm
TBD - Jake Solomon
Speaker: Jake Solomon, Hebrew University & Princeton University
Location:
Fine Hall 314
September 29, 2016
3:00pm - 4:00pm
Spanier-Whitehead $K$-duality

Classical Spanier-Whitehead duality was introduced for the stable homotopy category of finite CW complexes. We consider a noncommutative version, termed Spanier-Whitehead $K$-duality, which is defined on the category of $C^*$-algebras whose $K$-theory is finitely generated and that satisfy the UCT, with morphisms the Kasparov $KK$-groups. Examples from foliations, hyperbolic dynamics, and other highly non-commutative $C^*$-algebras illustrate the truly new phenomena encountered. There are many open questions associated with relaxing the assumptions on the algebras. For example, does the Calkin algebra have a Spanier-Whitehead $K$-dual? This is joint work with Jerry
Kaminker.

Speaker: Chaim Schochet, Technion University
Location:
Fine Hall 314
October 5, 2016
3:00pm - 4:00pm
TBD - Christos Mantoulidis
Speaker: Christos Mantoulidis, Stanford University
Location:
Fine Hall 314
October 6, 2016
3:00pm - 4:00pm
TBD - Kate Poirier
Speaker: Kate Poirier, CUNY/NYC College of Technology
Location:
Fine Hall 314
October 12, 2016
3:00pm - 4:00pm
TBD - Alexander Logunov
Speaker: Alexander Logunov , Tel Aviv University & St. Petersburg State University
Location:
Fine Hall 314
October 13, 2016
3:00pm - 4:00pm
TBD - Mark McConnell
Speaker: Mark McConnell, Princeton University
Location:
Fine Hall 314
October 17, 2016
4:30pm - 5:30pm
Quantum analogues of geometric inequalities for Information Theory

Note Special Date (but usual time and location)

Geometric inequalities, such as entropy power inequality or the isoperimetric inequality, relate geometric quantities, such as volumes and surface areas. Classically, these inequalities have useful applications for obtaining bounds on channel capacities, and deriving log-Sobolev inequalities. In my talk I provide quantum analogues of certain well-known inequalities from classical Information Theory, with the most notable being the isoperimetric inequality for entropies. The latter inequality is useful for the study of convergence of certain semigroups to fixed points. In the talk I demonstrate how to apply the isoperimetric inequality for entropies to show exponentially fast convergence of quantum Ornstein-Uhlenbeck (qOU) semigroup to a fixed point of the process. The inequality representing the fast convergence can be viewed as a quantum analogue of a classical Log-Sobolev inequality. As a separate result, necessary for the fast convergence of qOU semigroup, I argue that gaussian thermal states minimize output entropy for the attenuator semigroup among all states with a given mean-photon number. 

Speaker: Anna Vershynina, Basque Center for Applied Mathematics, Bilbao, Spain
Location:
Jadwin Hall 343
October 18, 2016
4:30pm - 5:30pm
TBD - V. Mastropietro
Speaker: V. Mastropietro, Università degli Studi di Milano
Location:
Jadwin Hall 343
October 19, 2016
3:00pm - 4:00pm
TBD - Mei-Chi Shaw
Speaker: Mei-Chi Shaw, University of Notre Dame
Location:
Fine Hall 314
October 25, 2016
4:30pm - 5:30pm
Can one hear the shape of a random walk?

We consider a Gibbs distribution over random walk paths on the square lattice, proportional to a random weight of the path’s boundary . We show that in the zero temperature limit, the paths condensate around an asymptotic shape. This limit shape is characterized as the minimizer of the functional, mapping open connected subsets of the plane to the sum of their principle eigenvalue and perimeter (with respect to the first passage percolation norm). A prime novel feature of this limit shape is that it is not in the class of Wulff shapes.
Joint work with Marek Biskup

Speaker: Eviatar Procaccia, Texas A&M
Location:
Jadwin Hall 343
October 26, 2016
3:00pm - 4:00pm
TBD - Celso Viana
Speaker: Celso Viana, Imperial College
Location:
Fine Hall 314
October 27, 2016
3:00pm - 4:00pm
TBD - Rade Zivaljevic
Speaker: Rade Zivaljevic, Serbian Academy of Sciences and Arts, Belgrade
Location:
Fine Hall 314
November 9, 2016
3:00pm - 4:00pm
TBD - Jim Isenberg
Speaker: Jim Isenberg, University of Oregon
Location:
Fine Hall 314
November 9, 2016
4:30pm - 5:30pm
TBD - Rafe Mazzeo
Speaker: Rafe Mazzeo, Stanford University
Location:
Fine Hall 314
November 16, 2016
3:00pm - 4:00pm
TBD - Chi Li
Speaker: Chi Li, Purdue University
Location:
Fine Hall 314
November 30, 2016
3:00pm - 4:00pm
TBD - Henri Roesch
Speaker: Henri Roesch, Duke University
Location:
Fine Hall 314
December 7, 2016
3:00pm - 4:00pm
TBD - Richard Bamler
Speaker: Richard Bamler, University of California, Berkeley
Location:
Fine Hall 314

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