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SUMMARY:Richard Stanley (Massachusetts Institute of Technology and Univers
 ity of Miami)
DTSTART:20250326T124000Z
DTEND:20250326T134000Z
DTSTAMP:20260422T213053Z
UID:BilkentMathematicsColloquium/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BilkentMathe
 maticsColloquium/1/">Some combinatorial applications of cyclotomic polynom
 ials</a>\nby Richard Stanley (Massachusetts Institute of Technology and Un
 iversity of Miami) as part of Bilkent Mathematics Colloquium\n\nLecture he
 ld in Zoom and Mathematics Seminar Room-SA141.\n\nAbstract\nWe begin with 
 three combinatorial results involving (1) partition\nidentities\, (2) coun
 ting polynomials over finite fields\, and (3)\nexpressing Dirichlet series
  in terms of the Riemann zeta\nfunction. These results can be unified usin
 g free monoids and extended\nusing cyclotomic polynomials. There is also a
  connection with\nnumerical semigroups (submonoids M of the nonnegative in
 tegers N under\naddition such that N-M is finite).\n\nTo request the Zoom 
 link\, please send an email to gokhan.yildirim@bilkent.edu.tr.\n
LOCATION:https://researchseminars.org/talk/BilkentMathematicsColloquium/1/
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SUMMARY:Lasse Grimmelt (University of Oxford)
DTSTART:20250416T134500Z
DTEND:20250416T144500Z
DTSTAMP:20260422T213053Z
UID:BilkentMathematicsColloquium/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BilkentMathe
 maticsColloquium/2/">The Primes and Additive Models</a>\nby Lasse Grimmelt
  (University of Oxford) as part of Bilkent Mathematics Colloquium\n\nLectu
 re held in Zoom and Mathematics Seminar Room-SA141.\n\nAbstract\nThe Hardy
 -Littlewood circle method is a powerful tool for additive problems\, as it
  helps separate signal from noise using Fourier analysis. When dealing wit
 h sums of primes (or their subsets)\, recent developments have focused on 
 extracting the signal not from the whole additive problem\, but separately
  for its constituents. This approach allows us to approximate a difficult 
 object\, such as the indicator function of the primes\, with a less comple
 x model.\n\nIn the first half of this talk\, I will explain these concepts
  in accessible terms and introduce useful approximants for the primes. In 
 the second half\, I will then sketch how these models play a role in upcom
 ing joint work with J. Teräväinen on sums of two Chen primes.\n\nTo requ
 est the Zoom link\, please send an email to gokhan.yildirim@bilkent.edu.tr
 .\n
LOCATION:https://researchseminars.org/talk/BilkentMathematicsColloquium/2/
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SUMMARY:Cihan Okay (Bilkent University)
DTSTART:20250507T124000Z
DTEND:20250507T134000Z
DTSTAMP:20260422T213053Z
UID:BilkentMathematicsColloquium/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BilkentMathe
 maticsColloquium/3/">Mathematics of Quantum Computational Advantage</a>\nb
 y Cihan Okay (Bilkent University) as part of Bilkent Mathematics Colloquiu
 m\n\nLecture held in Zoom and Mathematics Seminar Room-SA141.\n\nAbstract\
 nUnderstanding the origins of quantum computational advantage is a fundame
 ntal challenge in theoretical quantum computing. One direct approach to th
 is problem is through classical simulation algorithms. A celebrated result
  by Gottesman and Knill shows that quantum circuits built in the algebraic
  sub-theory of quantum mechanics\, the stabilizer theory\, can be efficien
 tly simulated on a classical computer. This theorem can be extended to bro
 ader classes of quantum circuits by employing sampling algorithms based on
  operator-theoretic polytopes. A natural framework for studying these simu
 lation polytopes and other foundational constructs in quantum theory is th
 e theory of simplicial distributions that extends the former sheaf-theoret
 ic approach of Abramsky and Brandenburger. Foundational notions\, such as 
 Bell's non-locality and its generalization quantum contextuality\, can be 
 interpreted as topological phenomena in this setting. Moreover\, Bell ineq
 ualities and extremal contextual distributions\, useful for quantum inform
 ation processing\, can be analyzed using simplicial methods from algebraic
  topology. In this talk\, I will present this diverse landscape\, highligh
 ting the intricate connections among algebraic topology\, polyhedral combi
 natorics\, and group theory in understanding quantum computational advanta
 ge.\n\nTo request the Zoom link\, please send an email to gokhan.yildirim@
 bilkent.edu.tr\n
LOCATION:https://researchseminars.org/talk/BilkentMathematicsColloquium/3/
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