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• Organizational Meeting

  Speaker: () -
  

  When: Tue, September 4, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  
• Harmonic analysis in combinatorics: a case study

  Speaker: Dong Dong (UMD) -
  

  When: Tue, September 11, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  

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  Abstract:
  The Roth theorem, which concerns the existence of three-term arithmetic progressions in certain sets, is a central topic in combinatorics. It also attracts researchers from different fields such as number theory, ergodic theory, analysis, and even computer science. In this talk, we will look at the Roth theorem from the harmonic analysis point of view. Surprisingly, harmonic analysis connects multilinear operators to very deep algebraic geometry. Although a few branches of mathematics are involved, this talk will be accessible to second-year graduate students and above.
  
  
• Constrictions of bent functions using a family of permutations and Reed-Muller type codes

  Speaker: Costas Karanikas (Aristotle University of Thessaloniki) - http://users.auth.gr/karanika/
  

  When: Tue, September 18, 2018 - 2:00pm
  Where: EGR 2116
  

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  Abstract: From a pair of permutations of the first n integers we get a family of permutations on 2^n objects. This family provides new bent functions ie Boolean sequences of length 2^(2n) whose Walsh transfom get values in {2^n,- 2^n}. The left half of a bent function determines a near-bent i.e., Boolean sequences of length 2^n (n odd) with Walsh spectrum in {0,2^n,-2^n} . We relate the support of near-bents with Reed - Muller type codes and using this we construct bents of higher degree using RM type codes and bents of lower type. We also discuss several ways for constructing bent functions and modify well-known constructions as for example Dillon H class and Maiorana- McFarland method .
  
• A sharp Schrodinger maximal estimate in R^2

  Speaker: Xiumin Du
  

  When: Tue, September 25, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  

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  Abstract: We consider Carleson’s pointwise convergence problem of Schrodinger solutions. It is shown that the solution to the free Schrodinger equation converges to its initial data almost everywhere, provided that the initial data is in the Sobolev space H^s(R^n) with s > n/2(n+1) (joint with Larry Guth and Xiaochun Li in the case n = 2, and joint with Ruixiang Zhang in the case n >= 3). This is sharp up to the endpoint, due to a counterexample by Bourgain. This pointwise convergence problem can be approached by estimates of Schrodinger maximal function, which have some similar flavors as the Fourier restriction/extension estimates. In this talk, we'll focus on the case $n=2$ and see how polynomial partitioning method and decoupling theorem play a role in such estimates.
  
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  When: Tue, October 2, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  
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  When: Tue, October 9, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  
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  When: Tue, October 16, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  
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  When: Tue, October 23, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  
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  When: Tue, October 30, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  
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  When: Tue, November 6, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  
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  When: Tue, November 13, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  
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  When: Tue, November 20, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  
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  When: Tue, November 27, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  
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  When: Tue, December 4, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  
• TBA

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  When: Tue, December 11, 2018 - 2:00pm
  Where: Kirwan Hall 3206