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Mathematics Department Colloquium : Spring 2012 schedule



   Monday, February 13, 1530-1630 (OBS! This is a promotion lecture).

SPEAKER : Peter Hegarty, Chalmers/GU.

TITLE : A whistle-stop personally guided tour through discrete mathematics.

ABSTRACT : As this is a promotion lecture, I am supposed to speak about my own research. I have worked in a number of different fields, though all my worthwhile results are essentially combinatorial in nature. If they are worth anything, it is probably that having worked in different fields has allowed me to spot some non-trivial connections between certain things, and hence some new results, that others would have missed. This will be the theme of my talk, which I will endeavour to illustrate with a number of examples drawing on additive number theory, graph theory, finite group theory and discrete probability.


   Monday, February 20, 1530 - 1630 (OBS! This is a promotion lecture).

SPEAKER : Mohammad Asadzadeh, Chalmers/GU.

TITLE : On the Fokker-Planck operator as an asymptotic limit and finite element methods for the Vlasov-Poisson-Fokker-Planck system.



   Monday, March 12, 1530 - 1630 (OBS! This is a promotion lecture).

SPEAKER : Aila Särkkä, Chalmers/GU.

TITLE : Analysis and modelling of spatial structure of epidermal nerve fibre patterns.

ABSTRACT : Epidermal nerve fiber (ENF) density and morphology are used to diagnose small fiber involvement in diabetic and other small fiber neuropathies. ENF density and summed length of ENFs per epidermal surface area are reduced, and ENFs may appear more clustered within the epidermis in subjects with small fiber neuropathy compared to healthy subjects. Therefore, it is important to understand the spatial behavior of ENFs in healthy and diseased subjects. We have investigated the spatial structure of ENF entry points, which are the locations where the nerves enter the epidermis (the outmost living layer of the skin). The study is based on suction skin blister specimens from two body locations of 25 healthy subjects. The ENF entry points are regarded as a realization of a spatial point process and a second-order characteristic, namely Ripley's $K$ function, is used to investigate the effect of covariates (e.g. gender) on the degree of clustering of ENF entry points. The effects of covariates and individual variation are characterized by a mixed model approach. We will also present some ideas about how to model the nerve entry point and end point structure.


   Monday, April 16, 1530 - 1630.

SPEAKER : Robert Berman, Chalmers/GU.

TITLE : Emergent complex geometry.

ABSTRACT : From a statistical mechanical point of view it is natural to view differential geometry as an emergent phenomena: the smooth shapes we see are emergent effects of some underlying microscopic model, as the number of particles tends to infinity. On the other hand, from a mathematical point of view it is also natural to view differential geometry as a limit of algebraic geometry, as the "degree" tends to infinity. Naively, this just amounts to the fact that any smooth curve can be approximated by a polynomial curve, but, in fact, this idea goes much deeper and is related to the fundamental "Yau-Tian-Donaldson conjecture" concerning Khler-Einstein metrics on projective algebraic varities. In this talk I will explain how these two different points of view on differential geometry can be merged, leading to a new probabilistic approach to Khler-Einstein metrics.


   Monday, April 23, 1530 - 1630.

SPEAKER : Daniel Persson, Department of Fundamental Physics, Chalmers.

TITLE : Crossing the wall: From geometry and number theory to physics.

ABSTRACT : I will give a survey of a universal phenomenon known as "wall-crossing" that occurs in a variety of different contexts, both in physics and in mathematics. The basic idea is that one studies objects which depend on a set of parameters, and these objects may "jump" discontinuously when crossing certain walls in the parameter space. The key problem is then to describe the change across the wall. Examples of such objects include the Euler characteristic on moduli spaces of sheaves, Donaldson-Thomas invariants of complex manifolds, and the particle spectrum of supersymmetric field theories. A general solution to the wall-crossing problem in the context of Donaldson-Thomas invariants was found recently by Kontsevich and Soibelman, but their solution appears to be universal and apply to many other situations as well. These results have opened up a host of new exciting developments and avenues of research on the borderline between physics and mathematics, involving hyperkähler geometry, cluster algebras, integrable systems, modular forms, and non-perturbative effects.


   Thursday, May 3, 1530 - 1630.

SPEAKER : Bruce Sagan, Michigan State University.

TITLE : Permutation patterns and statistics.



   Monday, May 28, 1530 - 1630.

SPEAKER : Olle Hggstrm, Chalmers/GU.

TITLE : The Great Filter: what statistical inference can we draw from one single bit of data ?.

ABSTRACT : This talk will try to make a coherent whole out of a hodgepodge of Bayesian reasoning, selection effects, Drake's equation, Fermi's paradox, exploratory engineering and evolutionary biology.


   Thursday, June 14, 1530 - 1630.

SPEAKER : Vladimir Korepin, Stony Brook.

TITLE : Quantum search.

ABSTRACT : Searching a database is an important problem in computer science. In 1997 Lov Grover discovered that quantum algorithms can perform database search faster than classical ones. I will explain a mathematical model for a database (including one-way functions). I will also explain different variations of Grover's search algorithm, including for circuits. The main principles of quantum mechanics will be recalled for the audience.