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SUMMARY:Richard Stanley (Massachusetts Institute of Technology and Univers
 ity of Miami)
DTSTART:20250326T124000Z
DTEND:20250326T134000Z
DTSTAMP:20260404T095847Z
UID:BilkentMathematicsColloquium/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Bilke
 ntMathematicsColloquium/1/">Some combinatorial applications of cyclotomic 
 polynomials</a>\nby Richard Stanley (Massachusetts Institute of Technology
  and University of Miami) as part of Bilkent Mathematics Colloquium\n\nLec
 ture held in Zoom and Mathematics Seminar Room-SA141.\n\nAbstract\nWe begi
 n with three combinatorial results involving (1) partition\nidentities\, (
 2) counting polynomials over finite fields\, and (3)\nexpressing Dirichlet
  series in terms of the Riemann zeta\nfunction. These results can be unifi
 ed using free monoids and extended\nusing cyclotomic polynomials. There is
  also a connection with\nnumerical semigroups (submonoids M of the nonnega
 tive integers N under\naddition such that N-M is finite).\n\nTo request th
 e Zoom link\, please send an email to gokhan.yildirim@bilkent.edu.tr.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathematicsColloq
 uium/1/
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SUMMARY:Lasse Grimmelt (University of Oxford)
DTSTART:20250416T134500Z
DTEND:20250416T144500Z
DTSTAMP:20260404T095847Z
UID:BilkentMathematicsColloquium/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Bilke
 ntMathematicsColloquium/2/">The Primes and Additive Models</a>\nby Lasse G
 rimmelt (University of Oxford) as part of Bilkent Mathematics Colloquium\n
 \nLecture held in Zoom and Mathematics Seminar Room-SA141.\n\nAbstract\nTh
 e Hardy-Littlewood circle method is a powerful tool for additive problems\
 , as it helps separate signal from noise using Fourier analysis. When deal
 ing with sums of primes (or their subsets)\, recent developments have focu
 sed on extracting the signal not from the whole additive problem\, but sep
 arately for its constituents. This approach allows us to approximate a dif
 ficult object\, such as the indicator function of the primes\, with a less
  complex model.\n\nIn the first half of this talk\, I will explain these c
 oncepts in accessible terms and introduce useful approximants for the prim
 es. In the second half\, I will then sketch how these models play a role i
 n upcoming joint work with J. Teräväinen on sums of two Chen primes.\n\n
 To request the Zoom link\, please send an email to gokhan.yildirim@bilkent
 .edu.tr.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathematicsColloq
 uium/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cihan Okay (Bilkent University)
DTSTART:20250507T124000Z
DTEND:20250507T134000Z
DTSTAMP:20260404T095847Z
UID:BilkentMathematicsColloquium/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Bilke
 ntMathematicsColloquium/3/">Mathematics of Quantum Computational Advantage
 </a>\nby Cihan Okay (Bilkent University) as part of Bilkent Mathematics Co
 lloquium\n\nLecture held in Zoom and Mathematics Seminar Room-SA141.\n\nAb
 stract\nUnderstanding the origins of quantum computational advantage is a 
 fundamental challenge in theoretical quantum computing. One direct approac
 h to this problem is through classical simulation algorithms. A celebrated
  result by Gottesman and Knill shows that quantum circuits built in the al
 gebraic sub-theory of quantum mechanics\, the stabilizer theory\, can be e
 fficiently simulated on a classical computer. This theorem can be extended
  to broader classes of quantum circuits by employing sampling algorithms b
 ased on operator-theoretic polytopes. A natural framework for studying the
 se simulation polytopes and other foundational constructs in quantum theor
 y is the theory of simplicial distributions that extends the former sheaf-
 theoretic approach of Abramsky and Brandenburger. Foundational notions\, s
 uch as Bell's non-locality and its generalization quantum contextuality\, 
 can be interpreted as topological phenomena in this setting. Moreover\, Be
 ll inequalities and extremal contextual distributions\, useful for quantum
  information processing\, can be analyzed using simplicial methods from al
 gebraic topology. In this talk\, I will present this diverse landscape\, h
 ighlighting the intricate connections among algebraic topology\, polyhedra
 l combinatorics\, and group theory in understanding quantum computational 
 advantage.\n\nTo request the Zoom link\, please send an email to gokhan.yi
 ldirim@bilkent.edu.tr\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathematicsColloq
 uium/3/
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