NTS Fall 2011/Abstracts: Difference between revisions
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 bgcolor="#F0A0A0" align="center" style="fontsize:125%"  '''Alexander Fish''' (Madison)   bgcolor="#F0A0A0" align="center" style="fontsize:125%"  '''Alexander Fish''' (Madison)  
    
 bgcolor="#BCD2EE" align="center"  Title:   bgcolor="#BCD2EE" align="center"  Title: Solvability of Diophantine equations within dynamically defined subsets of N  
    
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Abstract:  Abstract: Given a dynamical system, i.e. a compact metric space X, a homeomorphism T (or just a continuous map) and a Borel probability measure on X which is preserved under the action of T, the dynamically defined subset associated to a point x in X and an open set U in X is {n  T^n(x) is in U} which we call the set of return times of x in U. We study combinatorial properties of sets of return times for certain types of dynamical systems for generic points x in X. Among examples of such sets are normal sets which correspond to the system X = [0,1], T(x) = 2x mod 1, Lebesgue measure, U = [0, 1/2].  
We give a complete classification of linear Diophantine systems solvable within every normal set. The methods combine the probabilistic method together with the use of van der Corput's lemma. At the end of the talk we will discuss open problems  
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Revision as of 19:52, 22 August 2011
September 8
Alexander Fish (Madison) 
Title: Solvability of Diophantine equations within dynamically defined subsets of N 
Abstract: Given a dynamical system, i.e. a compact metric space X, a homeomorphism T (or just a continuous map) and a Borel probability measure on X which is preserved under the action of T, the dynamically defined subset associated to a point x in X and an open set U in X is {n  T^n(x) is in U} which we call the set of return times of x in U. We study combinatorial properties of sets of return times for certain types of dynamical systems for generic points x in X. Among examples of such sets are normal sets which correspond to the system X = [0,1], T(x) = 2x mod 1, Lebesgue measure, U = [0, 1/2]. We give a complete classification of linear Diophantine systems solvable within every normal set. The methods combine the probabilistic method together with the use of van der Corput's lemma. At the end of the talk we will discuss open problems 
September 15
Chung Pang Mok (McMaster) 
Title: Galois representation associated to cusp forms on GL_{2} over CM fields 
Abstract: We generalize the work of Harris–Soudry–Taylor, and constructs the compatible system of 2dimensional padic Galois representations associated to a cuspidal automorphic representation of cohomological type on GL_{2} over a CM field, whose central character satisfies an invariance condition. A localglobal compatibility statement, up to semisimplification, can also be proved in this setting. This work relies crucially on Arthur's results on lifting from the group GSp_{4} to GL_{4}.

September 22
Yifeng Liu (Columbia) 
Title: tba 
Abstract: tba 
September 29
Nigel Boston (Madison) 
Title: tba 
Abstract: tba 
October 6
Zhiwei Yun (MIT) 
Title: tba 
Abstract: tba 
October 27
Zev Klagsburn (Madison) 
Title: tba 
Abstract: tba 
November 17
Robert Harron (Madison) 
Title: tba 
Abstract: tba 
December 8
Xinwen Zhu (Harvard) 
Title: tba 
Abstract: tba 
Organizer contact information
Zev Klagsbrun
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