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DTSTART:20070311T020000
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DTSTAMP:20260920T131702
DTSTART;TZID=America/Detroit:20261002T150000
DTEND;TZID=America/Detroit:20261002T160000
SUMMARY:Lecture / Discussion:AIM Seminar:  Math and physics at the moiré scale
DESCRIPTION:Abstract: Placing a two-dimensional lattice with a small rotation gives rise to almost periodic \"moiré\" patterns on a superlattice scale much larger than the original lattice. We have used the mathematical techniques developed to study waves in inhomogeneous media to identify a regime where the Bistritzer-MacDonald continuum model emerges as the effective dynamics for electrons modeled as wave-packets spectrally concentrated at the monolayer Dirac points of linear dispersion\, up to error that we rigorously estimate. We have shown that this regime is realized in twisted bilayer graphene at the first \"magic\" angle where the group velocity of the wave packet is zero and strongly correlated electronic phases (superconductivity\, Mott insulators\, etc.) have recently been observed.\n\nWe will present recent results that rigorously extend this analysis to account for the effects of structural relaxation and to essentially arbitrary moiré materials such as twisted multilayer transition metal dichalcogenides (TMDs) or even twisted heterostructures consisting of layers of distinct 2D materials.\n\nContact: Ian Tobasco
UID:148876-21905038@events.umich.edu
URL:https://events.umich.edu/event/148876
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Applied Mathematics,Mathematics
LOCATION:East Hall - 1084
CONTACT:
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DTSTAMP:20260914T092752
DTSTART;TZID=America/Detroit:20261002T150000
DTEND;TZID=America/Detroit:20261002T160000
SUMMARY:Workshop / Seminar:Combinatorial invariance for the coefficient of q in Kazhdan-Lusztig polynomials
DESCRIPTION:I will describe joint work with Grant Barkley and Thomas Lam in which we study the Combinatorial Invariance Conjecture (CIC)\, which asserts that Kazhdan-Lusztig polynomials depend only on the combinatorics of Bruhat order. Motivated by the cluster structure on Richardson varieties\, we prove the combinatorial invariance of the coefficient of q in KL polynomials for arbitrary Coxeter groups. We also prove the Gabber-Joseph conjecture for the second-highest Ext group of a pair of Verma modules\, as well as the combinatorial invariance of the dimension of this group.
UID:149734-21907011@events.umich.edu
URL:https://events.umich.edu/event/149734
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4088
CONTACT:
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