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Autumn Semester 2026

Date / Time Speaker Title Location
22 September 2026
16:30-18:15 		Gabriella Tarantello
University Rom Tor Vergata
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Zurich Colloquium in Mathematics

Title On CMC 1-immersions of a closed surface into hyperbolic 3-manifolds
Speaker, Affiliation Gabriella Tarantello, University Rom Tor Vergata
Date, Time 22 September 2026, 16:30-18:15
Location KO2 F 150
Abstract Constant Mean Curvature (CMC) c-immersions of a closed orientable surface S (with genus g ≥ 2) into hyperbolic 3-manifolds emerged by the work of K. Uhlenbeck in connection with irreducible representations of the fundamental group of S into the Mobious group. For |c| < 1, such (CMC) c-immersions are always available and labelled by elements of the tangent bundle of the Teichmueller space of S. On the other hand, the (critical) value |c|=1 of the mean curvature plays a crucial role, since (CMC) 1-immersions into the hyperbolic space H^3 (known as Bryant surfaces) furnish the hyperbolic analogue (via bi-holomorphisms) of the classical minimal immersions into the Euclidean 3-space E^3. Naturally, one could try to attain (CMC) 1-immersions as limits for |c| → 1. But possible “blow-up” phenomena could yield (after scaling) to (CMC) 1-immersions with conical singularities, consistently with the presence of smooth ends in Bryant surfaces. I shall discuss how to encompass the blow-up situation in terms of suitable “orthogonality conditions” involving the image Z of the Kodaira map (for genus g = 2) and more generally the (g −1)-secant variety of Z, for larger genus. Subsequently, using Hitchin self-duality theory, I shall indicate how the given “orthogonality conditions” are actually sharp towards “compactness”. In this way, under a generic condition, we can ensure existence and uniqueness of (CMC) 1-immersions of S into (germs) of hyperbolic 3-manifolds, and obtain a parametrization of the corresponding moduli space in terms of the tangent bundle of the Teichmueller space of S.
On CMC 1-immersions of a closed surface into hyperbolic 3-manifoldsread_more
KO2 F 150
29 September 2026
16:30-18:15 		Emily Riehl
Johns Hopkins University
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Zurich Colloquium in Mathematics

Title A reintroduction to proofs
Speaker, Affiliation Emily Riehl, Johns Hopkins University
Date, Time 29 September 2026, 16:30-18:15
Location KO2 F 150
Abstract This talk proposes a shift in the implicit foundations of mathematics from set theory and logic to dependent type theory (where the primitive notion of “type” replaces both sets and propositions). While these new foundations are more complex, we contend they make it easier for students to learn to write correct proofs and for professionals to communicate precise mathematical ideas to other humans or to a computer.
A reintroduction to proofsread_more
KO2 F 150
3 November 2026
16:30-18:15 		Amol Aggarwal
Stanford University
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Zurich Colloquium in Mathematics

Title Many Body Asymptotics for the Toda Lattice
Speaker, Affiliation Amol Aggarwal, Stanford University
Date, Time 3 November 2026, 16:30-18:15
Location KO2 F 150
Abstract The Toda lattice prescribes the evolution of many particles interacting under certain Hamiltonian dynamics; it is an archetypal example of a completely integrable system. In this talk we describe several results providing the long-time asymptotics of this system, under random, dense initial data. The proofs proceed by finding a way to interpret the Toda lattice as a collection of "quasi-particles" that behave similarly to solitons, and providing a framework to study how these quasi-particles asymptotically evolve in time. The arguments use ideas from random matrix theory, particularly the analysis of Lyapunov exponents governing the decay rates of eigenvectors of random tridiagonal matrices.
Many Body Asymptotics for the Toda Latticeread_more
KO2 F 150

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