ALGEBRAIC DYNAMICS
September 23, 2021 4:00 pmGiven 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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OPEN NEIGHBORHOOD
September 22, 2021 4:30 pmProjective 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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SEMINARS, NUMBER THEORY
September 22, 2021 3:00 pmGiven a variety over a number field, its geometric etale fundamental group comes equipped with an action of the Galois group. This induces a Galois action on the pro-algebraic completion...
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HARVARD-MIT ALGEBRAIC GEOMETRY
September 21, 2021 3:00 pmAlgebraic 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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NUMBER THEORY
September 15, 2021 3:00 pmWe 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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HARVARD-MIT ALGEBRAIC GEOMETRY
September 14, 2021 3:00 pmThe 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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ALGEBRAIC DYNAMICS
September 9, 2021 4:00 pmMotivated 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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OPEN NEIGHBORHOOD
September 8, 2021 4:30 pmInteresting 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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NUMBER THEORY
September 8, 2021 3:00 pmThe p-torsion in the class group of a number field K is conjectured to be small: of size at most |Disc K|^epsilon, and to have constant average size in families...
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ALGEBRAIC DYNAMICS
August 26, 2021 3:00 pmThe 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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