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See also the PSU Calendars
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A live feed of seminars and special events in the upcoming week.
- January 13th, 2009 (02:30pm - 03:45pm)
- Seminar: Logic Seminar
Title: Proof mining in topological dynamics
Speaker: Philipp Gerhardy, University of Oslo
Location: MB315The Multiple Birkhoff Recurrence theorem by Furstenberg and Weiss in 1978 is a seminal result for the interaction between topological dynamics and combinatorics, establishing Ramsey-type theorems through corresponding recurrence results. However, while combinatorial proofs often contain explicit quantitative information, topological proofs usually do not contain realizers, bounds or similar data. E.g. for van der Waerden's theorem -- for every finite colouring of the integers one colour contains arbitrarily long arithmetic progressions -- one may ask for a number N = N(q; k) such that for every q-colouring of [0;N] one colour contains a progression of length k. The combinatorial proof contains an explicit upper bound on N(q; k), while Furstenberg and Weiss' topological proof does not. Thus one may ask: what is the algorithmic content of the topological proofs of Ramsey-type theorems. We will present an analysis of Furstenberg and Weiss' Multiple Birkhoff Recurrence theorem which generalizes a previous analysis by Girard. We will also discuss the use of compactness in proofs of the Multiple Birkhoff Recurrence theorem, i.e. the concept of minimality in topological dynamics, sketch the treatment of generalizations of the Multiple Birkhoff Recurrence theorem, and, if time permits, survey some related proof mining results in ergodic theory.
- January 13th, 2009 (03:30pm - 06:00pm)
- Seminar: Working Seminar: Dynamics and its Working Tools
Title: Lusternik-Shnirelman Theorem on three closed geodescs on a sphere, I.
Speaker: Dmitry Scheglov
Location: MB216 - January 20th, 2009 (02:30pm - 03:45pm)
- Seminar: Logic Seminar
Title: Self-referential constructions, fixed-point theorems, and aperiodic tilings
Speaker: Alexander Shen, LIF (Marseille) and IITP (Moscow)
Location: MB315We shall discuss the following topics: Wang tiles and the domino problem, aperiodic tile sets, history (Berger, Robinson, Penrose, Ammann, Kari, ...), aperiodicity of self-similar tilings, self-similar tilings and the theory of computation (implementing a given tile set), self-referential constructions and fixed-point results in logic and computer science, a self-implementing tile set. As applications we shall discuss strongly aperiodic tilings, robust aperiodic tilings, a simple proof of undecidability of the domino problem, and high-complexity tilings.
- January 20th, 2009 (03:30pm - 06:00pm)
- Seminar: Working Seminar: Dynamics and its Working Tools
Title: Lusternik-Shnirelman Theorem on three closed geodescs on a sphere, II.
Speaker: Dmitry Scheglov
Location: MB216 - January 22nd, 2009 (11:15am - 12:05pm)
- Seminar: Algebra and Number Theory Seminar
Title: Families of hyperelliptic jacobians without complex multiplication
Speaker: Yuri Zarhin, Penn State University
Location: MB106 - January 22nd, 2009 (04:00pm - 05:00pm)
- Seminar: Department of Mathematics Colloquium
Title: Algorithmic randomness
Speaker: Alexander Shen, University of Marseille and Institute for Information Transmission Problems, Moscow
Location: MB114Plan of the talk: Motivation: why would we like to define a notion of an individual random object? Classical probability theory and its relation to the "real world''. Cournot principle. Frequency approach to randomness (von Mises). Selection rules and collectives. Constructive measure theory approach (Martin-Lof) Description (Kolmogorov) complexity, incompressibility and randomness Pseudo-random sequences: time-bounded complexity, Yao-Blum-Micali generators
- January 26th, 2009 (11:15am - 12:15pm)
- Seminar: The Pritchard Lab Seminar
Title: TBA
Speaker: Sebastian Schreiber, Department of Evolution & Ecology, UC Davis
Location: MB106 - January 27th, 2009 (03:30pm - 06:00pm)
- Seminar: Working Seminar: Dynamics and its Working Tools
Title: Exponential error term for the growth of closed geodesics on negatively curved surfaces; after Dolgopyat and Pollicott-Sharp, II.
Speaker: Pavlo Tsytsura
Location: MB216 - January 29th, 2009 (04:00pm - 05:00pm)
- Seminar: Department of Mathematics Colloquium
Title: TBA
Speaker: David Vogan, MIT
Location: MB101