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DTSTAMP:20260922T115750
DTSTART;TZID=America/Detroit:20260930T153000
DTEND;TZID=America/Detroit:20260930T165000
SUMMARY:Workshop / Seminar:Algebraic Geometry Seminar: Crepant resolutions via stacks
DESCRIPTION:Consider an invariant that behaves nicely for smooth varieties\, such as Euler number\, Betti numbers\, or Hodge numbers. Suppose we want a version of this invariant for singular varieties that sees interesting information about the singularities. I will discuss how this naturally leads to the notion of crepant resolutions of singularities. However\, crepant resolutions (by varieties) are rare in practice. I will discuss joint work with M. Satriano in which we show that crepant resolutions actually exist in broad generality\, as long as one is willing to consider algebraic stacks. Specifically\, any variety with log-terminal singularities admits a crepant resolution by a smooth algebraic stack. As one consequence\, in joint work with J. Huang and M. Satriano\, we obtain a cohomological interpretation for Batyrev's stringy Hodge numbers. This talk will not assume familiarity with stacks.
UID:149657-21906898@events.umich.edu
URL:https://events.umich.edu/event/149657
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4096
CONTACT:
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DTSTAMP:20260924T111012
DTSTART;TZID=America/Detroit:20260930T160000
DTEND;TZID=America/Detroit:20260930T170000
SUMMARY:Workshop / Seminar:CCMB/DCMB Weekly Bioinformatics Seminar Series featuring Jianzhi Zhang\, PhD (Professor\, Ecology and Evolutionary Biology\, U-M)
DESCRIPTION:Jianzhi (George) Zhang is a Professor of Ecology and Evolutionary Biology interested in the relative roles of chance and necessity in evolution. He got his B. S. from Fudan University in Shanghai\, China\, and his Ph. D. in Genetics from Pennsylvania State University. He was a  Fogarty postdoctoral fellow at the National Institute of Allergy and Infectious Diseases before moving to the University of Michigan.\n\nAbstract\n\nAdaptive evolution proceeds through beneficial nucleotide substitutions in the genome\, yet the number of such substitutions (N) required to reach a local or global fitness peak where no single mutation further increases fitness remains unknown. Here we estimate N by simulating adaptive walks on two large\, complete\, multi-environment adaptive landscapes inferred from massive empirical data using machine learning\, with validation from smaller experimentally mapped landscapes. We find that N rises linearly with the number of variable sites (L) in the landscape\, regardless of prior adaptation in another environment. Extrapolation suggests a minimal N of 10^5 for typical prokaryotes and 10^7 for mammals. By contrast\, in highly rugged shuffled landscapes\, N is markedly reduced\, while fitness gains also shrink. The relatively smooth empirical landscapes therefore enable greater fitness gains while lengthening adaptive walks\, rendering even local fitness peaks effectively unreachable before environments change. These results explain the persistence of fitness gains in long-term evolution experiments and the widespread occurrence of beneficial mutations across species. They suggest that populations continuously adapt while remaining far from fitness optima\, challenging the long-held view that adaptation culminates at fitness peaks.
UID:150650-21909759@events.umich.edu
URL:https://events.umich.edu/event/150650
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Genome,Ecology,Biosciences,Biology,Bioinformatics,Basic Science
LOCATION:Medical Science Unit I - 4B700
CONTACT:
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