13:15-14:00: |
Speaker: John Man Shun Ma (U Copenhagen) |
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| Title: On the compactness of Hamiltonian stationary Lagrangian submanifolds | |||
| Abstract: Let $(M,\omega)$ be a symplectic manifold with a compatible metric. A Lagrangian submanifold in $M$ is called Hamiltonian stationary (HSL) if it is a critical point of the volume functional among Hamiltonian Variations. In this talk, we discuss two compactness theorems on the space of HSL submanifold with uniformly bounded area and total extrinsic curvature. This is a joint work with Jingyi Chen. | |||
14:00-14:30: |
Speaker: Jingxuan Zhang (U Copenhagen) [Via Zoom from Boston] |
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| Title: Quasi-locality and recursive monotonicity estimates for quantum evolutions | |||
| Abstract: Pseudolocality theorems and monotonicity estimates are powerful tools in the study of geometric flows, as they impose general constraints on evolving geometric objects that are otherwise hard to keep track of. In this talk, we present parallel results for quantum evolutions modeled by a large class of time-dependent Schrödinger equations. Specifically, we consider nonlocal non-autonomous Schrödinger equations, for which the Hamiltonians consist of nonlocal diffusion operators and arbitrary bounded time-dependent potentials. We prove that states evolving according to these Schrödinger equations can be approximated by strictly localized states in an explicit light cone for all time, with asymptotically vanishing error. This result follows from monotonicity estimates for a class of observables that identify the propagation of states. | |||
| 14:30-15:15 |
Break - Coffee/tea and cookies |
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15:15-16:00: |
Speaker: Mateo Galdeano (U Hamburg) |
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| Title: Superconformal Algebras for (Generalized) Connected Sums | |||
| Abstract: When string theory is compactified on special holonomy manifolds, a fascinating correspondence arises: covariantly constant forms are associated to operators in the worldsheet chiral algebra. I will discuss this relation in the context of Generalized Connected Sum Spin(7) manifolds, which are constructed by gluing together two open manifolds along isomorphic asymptotic ends. The geometric structure is reproduced in the worldsheet algebra, and this can be exploited to shed some light on the properties of these manifolds, including the possibility of Spin(7) mirror symmetry. This talk is based on joint work with M.-A. Fiset, [2104.05716]. | |||
16:00-16:30: |
Speaker: Alejandro Gil-Garcia (U Hamburg) |
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| Title: A class of locally inhomogeneous complete quaternionic Kähler manifolds | |||
| Abstract: We prove that the one-loop deformation of any quaternionic Kähler manifold in the class of c-map spaces is locally inhomogeneous. As a corollary, we obtain that the full isometry group of the one-loop deformation of any homogeneous c-map space has precisely cohomogeneity one. This is a joint work with Vicente Cortés and Arpan Saha (see https://arxiv.org/abs/2210.10097). |
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| TBA |
Walk + Dinner |
11:15-12:15: |
Speaker: Huy The Nguyen (Queen Mary) |
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| Title: A Brakke type regularity theorem for the Allen-Cahn flow | |||
| Abstract: We will consider the relationship between the Allen-Cahn flow, a semilinear parabolic PDE and the mean curvature flow. In particular, we will show an analogue of the Brakke's local regularity theorem for the Allen-Cahn flow that is we show uniform $C^{2,\alpha}$ regularity for the transition layers converging to smooth mean curvature flows as $\varepsilon$ tends to $0$ under an almost unit-density assumption and show how to use this theorem to answer a question of Ilmanen on no cancellation in the limit. We will also discuss some more recent relations between these two equations. This talk is based on joint work with Shengwen Wang. | |||
| 12:15-13:15 |
Break - Lunch |
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13:15-14:15: |
Speaker: Alexander Mramor (U Copenhagen) |
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| Title: Some new applications of the mean curvature flow to self-shrinkers. | |||
| Abstract: In this talk I’ll discuss some applications of the mean curvature flow to asymptotically conical self shrinkers in R^3 and R^4. | |||
| 14:15-15:15 |
Break - Coffee/tea and cookies |
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15:15-16:15: |
Speaker: Mario Schulz (U Münster) |
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| Title: Free boundary minimal surfaces in the unit ball | |||
| Abstract: Free boundary minimal surfaces arise naturally in partitioning problems for convex bodies, in capillarity problems for fluids and in the study of extremal metrics for Steklov eigenvalues on manifolds with boundary. The theory has been developed in various interesting directions, yet many fundamental questions remain open. Two of the most basic ones can be phrased as follows: (1) Can a surface of any given topology be realised as an embedded free boundary minimal surface in the 3-dimensional Euclidean unit ball? We answer this question affirmatively for surfaces with connected boundary and arbitrary genus. (2) When they exist, are such embeddings unique up to ambient isometry? We answer this question in the strongest negative terms by providing pairs of non-isometric free boundary minimal surfaces with the same topology and symmetry group. (Joint work with Alessandro Carlotto and Giada Franz respectively David Wiygul.) | |||
| 20:30- |
Dinner |