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Quantitative Logarithmic Equidistribution and S-Integrality

ALGEBRAIC DYNAMICS

September 23, 2021      4:00 pm
Speaker: Jit Wu Yap - Harvard University

Given a rational map defined over a number field, the Galois orbits of points with canonical height tending to zero will equidistribute to a measure supported on the Julia set....
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Projective vs. abelian geometry

OPEN NEIGHBORHOOD

September 22, 2021      4:30 pm
Speaker: Mihnea Popa - Harvard University

Projective space and complex tori are two of the simplest types of manifolds we encounter, and in many ways they seem very different from each other. I will try to...
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Tautological classes of matroids

HARVARD-MIT ALGEBRAIC GEOMETRY

September 21, 2021      3:00 pm
Speaker: Christopher Eur - Harvard University

Algebraic geometry has furnished fruitful tools for studying matroids, which are combinatorial abstractions of hyperplane arrangements.  We first survey some recent developments, pointing out how these developments remained partially disjoint....
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Finitely Presented Groups in Arithmetic Geometry

NUMBER THEORY

September 15, 2021      3:00 pm
Speaker: Mark Shusterman - Harvard University

We discuss the problem of determining the number of generators and relations of several profinite groups of arithmetic and geometric origin. These include etale fundamental groups of smooth projective varieties,...
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Measuring the irrationality of complete intersections

HARVARD-MIT ALGEBRAIC GEOMETRY

September 14, 2021      3:00 pm
Speaker: Nathan Chen - Harvard University

The classical question of determining which varieties are rational has led to a huge amount of interest and activity. On the other hand, one can take on a complementary perspective:...
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On the dynamical Bogomolov conjecture

ALGEBRAIC DYNAMICS

September 9, 2021      4:00 pm
Speaker: Myrto Mavraki - Harvard University

Motivated by the Manin-Mumford and the Bogomolov conjecture for abelian varieties, Zhang conjectured that an analogous statement holds in a more general dynamical setting. In this talk we discuss various...
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Prime numbers and Julia sets

OPEN NEIGHBORHOOD

September 8, 2021      4:30 pm
Speaker: Laura DeMarco - Harvard University

Interesting patterns of prime numbers can arise in recursively defined sequences (such as the Fibonacci sequence). For non-linear recursions, there are intriguing connections with complex dynamics and the Mandelbrot set....
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The pentagram map and the arithmetic of abelian varieties

ALGEBRAIC DYNAMICS

August 26, 2021      3:00 pm
Speaker: Max Weinreich - Brown University

The pentagram map was introduced by Schwartz as a dynamical system on polygons in the real projective plane. The map sends a polygon to the shape formed by intersecting certain...
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