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DTSTART;TZID=America/New_York:20260202T150000
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DTSTAMP:20260513T084236
CREATED:20251223T185600Z
LAST-MODIFIED:20260126T185935Z
UID:10003816-1770044400-1770048000@cmsa.fas.harvard.edu
SUMMARY:Reflexive Polytopes and the Convergence of Feynman Integrals
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \nSpeaker: Pierre Vanhove (Institute of Theoretical Physics – Saclay) \nTitle: Reflexive Polytopes and the Convergence of Feynman Integrals \nAbstract: In the parametric representation\, Feynman integrals can be viewed as Euler integrals defined by the Symanzik polynomials of a graph. The convergence properties of these integrals are intimately tied to the combinatorial geometry of their associated Newton polytopes; specifically\, finiteness is guaranteed when the polytope contains interior points. We present a classification of Feynman integrals associated with polytopes containing a unique interior point\, identifying a subset that are reflexive. Our results show that such reflexive polytopes are surprisingly scarce within the space of Feynman graphs. We conclude by computing several infinite families of these integrals and exploring their connections to mirror symmetry and toric geometry. This is based on joint work with Leonardo de la Cruz and Pavel Novichkov.
URL:https://cmsa.fas.harvard.edu/event/qft_2226/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QFT-and-Physical-Mathematics-2.2.26-scaled.png
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DTSTART;TZID=America/New_York:20260202T163000
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DTSTAMP:20260513T084236
CREATED:20251223T190540Z
LAST-MODIFIED:20260122T163725Z
UID:10003849-1770049800-1770053400@cmsa.fas.harvard.edu
SUMMARY:Bijections for hyperplane arrangements of Coxeter type
DESCRIPTION:Colloquium \nSpeaker: Olivier Bernardi\, Brandeis University \nTitle: Bijections for hyperplane arrangements of Coxeter type \nAbstract: This talk is about real hyperplane arrangements whose hyperplanes are of the form {xi −xj = s} or {xi +xj = s}. We describe a bijective framework for a large family of such arrangements which we call transitive. For each transitive arrangement A\, we give a bijection between the regions of A and a set of decorated trees. Particular cases include the families of Catalan\, Shi\, semiorder and Linial arrangements in type A\, B\, C\, D and BC. We also derive some general enumerative formulas for such families of transitive arrangements.
URL:https://cmsa.fas.harvard.edu/event/colloquium-2226/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
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