Zurich colloquium in mathematics

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Date / Time

Speaker

Title

Location

4 October 2016
17:15-18:15

Dr. Maryna Viazovska
Humbold Universität Berlin

Details

Title	The sphere packing problem in dimensions 8 and 24
Speaker, Affiliation	Dr. Maryna Viazovska, Humbold Universität Berlin
Date, Time	4 October 2016, 17:15-18:15
Location	KO2 F 150
Abstract	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.

The sphere packing problem in dimensions 8 and 24read_more

KO2 F 150

25 October 2016
17:15-18:15

Prof. Dr. Eitan Tadmor
University of Maryland + ETH-ITS

Details

Title	Collective dynamics: emergence of consensus and social hydrodynamics
Speaker, Affiliation	Prof. Dr. Eitan Tadmor , University of Maryland + ETH-ITS
Date, Time	25 October 2016, 17:15-18:15
Location	KO2 F 150
Abstract	Prototypical models for collective dynamics are found in opinion dynamics, flocking, self-organization of biological organisms, and rendezvous in mobile networks. They are driven by the “social engagement” of agents with their local neighbors. We discuss the emergent behavior of such systems. Their large-time behavior leads to the emergence of different patterns, depending on the propagation of connectivity of the underlying graphs. In particular, global interactions lead to the emergence of consensus, leaders etc. The collective dynamics of large crowds of agents lend itself to “social hydrodynamics”, driven by the corresponding local means. We discuss the global regularity of social hydrodynamics for sub-critical initial configurations.

Collective dynamics: emergence of consensus and social hydrodynamicsread_more

KO2 F 150

15 November 2016
17:15-18:15

Prof. Dr. Kaisa Matomäki
University of Turku

Details

Title	Around the Möbius function
Speaker, Affiliation	Prof. Dr. Kaisa Matomäki , University of Turku
Date, Time	15 November 2016, 17:15-18:15
Location	KO2 F 150
Abstract	The Möbius function plays a central role in number theory; both the prime number theorem and the Riemann Hypothesis are naturally formulated in terms of the amount of cancellation one gets when summing the Möbius function. In a joint work with Maksym Radziwill we have shown that the sum of the Möbius function exhibits cancellation in "almost all intervals" of arbitrarily slowly increasing length. This goes beyond what was previously known conditionally on the Riemann Hypothesis. Ourresult holds in fact for much more general multiplicative functions, andhas several further applications, many of which I will discuss in the talk.

Around the Möbius functionread_more

KO2 F 150

6 December 2016
17:15-18:15

Prof. Dr. Emmy Murphy
Massachusetts Institute of Technology

Details

Title	A contact topologist's perspective on mirror symmetry
Speaker, Affiliation	Prof. Dr. Emmy Murphy , Massachusetts Institute of Technology
Date, Time	6 December 2016, 17:15-18:15
Location	KO2 F 150
Abstract	Generally speaking, mirror symmetry is some kind of duality between complex algebraic geometry and symplectic geometry. Many approaches to mirror symmetry focus on manifolds with large symmetry actions (ie toric manifolds), and everything reduces to the algebra of the symmetry group. This talk will focus on the opposite approach: we will seek to understand symplectic manifolds from a topologist's perspective, which brings us into the world of contact geometry and Weinstein handlebody theory. Once we have a picture of the manifold's structure we can play with it, simplify it, and eventually see all the algebra of mirror symmetry visually.

A contact topologist's perspective on mirror symmetryread_more

KO2 F 150

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