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DTSTART;TZID=America/New_York:20220503T093000
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UID:10002557-1651570200-1651573800@cmsa.fas.harvard.edu
SUMMARY:The threshold for stacked triangulations
DESCRIPTION:Abstract: Consider a bootstrap percolation process that starts with a set of `infected’ triangles $Y \subseteq \binom{[n]}3$\, and a new triangle f gets infected if there is a copy of K_4^3 (= the boundary of a tetrahedron) in which f is the only not-yet infected triangle.\nSuppose that every triangle is initially infected independently with probability p=p(n)\, what is the threshold probability for percolation — the event that all triangles get infected? How many new triangles do get infected in the subcritical regime? \nThis notion of percolation can be viewed as a simplification of simple-connectivity. Namely\, a stacked triangulation of a triangle is obtained by repeatedly subdividing an inner face into three faces.\nWe ask: for which $p$ does the random simplicial complex Y_2(n\,p) contain\, for every triple $xyz$\, the faces of a stacked triangulation of $xyz$ whose internal vertices are arbitrarily labeled in [n]. \nWe consider this problem in every dimension d>=2\, and our main result identifies a sharp probability threshold for percolation\, showing it is asymptotically (c_d*n)^(-1/d)\, where c_d is the growth rate of the Fuss–Catalan numbers of order d. \nThe proof hinges on a second moment argument in the supercritical regime\, and on Kalai’s algebraic shifting in the subcritical regime. \nJoint work with Eyal Lubetzky.
URL:https://cmsa.fas.harvard.edu/event/5-3-2022-cmsa-combinatorics-physics-and-probability-seminar/
LOCATION:Hybrid
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-05.03.22-1.png
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DTSTART;TZID=America/New_York:20220419T093000
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DTSTAMP:20260417T001637
CREATED:20240214T070331Z
LAST-MODIFIED:20240304T084706Z
UID:10002554-1650360600-1650364200@cmsa.fas.harvard.edu
SUMMARY:Some combinatorics of Wilson loop diagrams
DESCRIPTION:Abstract: Wilson loop diagrams can be used to study amplitudes in N=4 SYM.  I will set them up and talk about some of their combinatorial aspects\, such as how many Wilson loop diagrams give the same positroid and how to combinatorially read off the dimension and the denominators for the integrands. \n**This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10. \nAll non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival. \nLINK TO FORM
URL:https://cmsa.fas.harvard.edu/event/4-19-2022-combinatorics-physics-and-probability-seminar/
LOCATION:Hybrid
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-04.19.22.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210301T100000
DTEND;TZID=America/New_York:20210301T110000
DTSTAMP:20260417T001637
CREATED:20240126T083833Z
LAST-MODIFIED:20240126T083848Z
UID:10001417-1614592800-1614596400@cmsa.fas.harvard.edu
SUMMARY:Mathematical supergravity and its applications to differential geometry
DESCRIPTION:Speaker: Carlos S. Shahbazi (Hamburg University) \nTitle: Mathematical supergravity and its applications to differential geometry \nAbstract: I will discuss the recent developments in the mathematical theory of supergravity that lay the mathematical foundations of the universal bosonic sector of four-dimensional ungauged supergravity and its Killing spinor equations in a differential-geometric framework.  I will provide the necessary context and background. explaining the results pedagogically from scratch and highlighting several open mathematical problems which arise in the mathematical theory of supergravity\, as well as some of its potential mathematical applications. Work in collaboration with Vicente Cortés and Calin Lazaroiu.
URL:https://cmsa.fas.harvard.edu/event/3-1-2021-mathematical-physics-seminar/
LOCATION:Hybrid
CATEGORIES:Mathematical Physics Seminar
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