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Dan Freed (University of Austin)22/05/2023, 09:30
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Andras Stipsicz22/05/2023, 10:45
We will review the genus function (associating to a second homology class the minimal genus of an embedded surface representing it), and show how to extend it. The function turns out to be useful in obstructing smooth sliceness, while the extension might become handy in contemplating
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about smooth structures on the four-sphere. -
Arunima Ray (Max Planck Institute for Mathematics)22/05/2023, 11:35
I will describe a general procedure to homotope an immersed positive genus surface in a simply connected 4-manifold to a locally flat embedding. This is a special case of a surface embedding theorem, joint with Daniel Kasprowski, Mark Powell, and Peter Teichner.
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Thomas Nikolaus (University of Münster)22/05/2023, 21:00
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David Reutter23/05/2023, 09:30
How much manifold topology can a given topological quantum field theory see? In this talk, I will answer this question for "semisimple" TQFTs in even dimensions, a certain class of field theories which includes all "once-extended" even-dimensional field theories, i.e. those which also assign linear categories to corners of codimension 2.
These results suggest to think of TQFTs as...
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Daniel Kasprowski (University of Southampton)23/05/2023, 10:45
I will introduce and study relations of 4-manifolds up to connected sum with copies of $S^2\times S^2$ and their relations. This includes stable diffeomorphism and homotopy equivalence. The talk is based on joint work with Johnny Nicholson and Simona Veselá.
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Markus Land23/05/2023, 11:35
I propose to present a construction of a Poincare duality space with the two properties: 1) its Spivak normal fibration does not admit a Top-reduction (equivalently, there is no degree one normal map from a topological closed manifold) and 2) its (periodic) total surgery obstruction vanishes. This contradicts the validity of two theorems in the literature, the one stating that PD complexes...
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Matt Hedden23/05/2023, 21:00
Chern-Simons invariants of homology spheres, analyzed in conjunction with moduli spaces of solutions to the ASD Yang-Mills equations on 4-manifolds, provide a powerful tool for studying the homology cobordism groups of 3-manifolds and the closely related smooth concordance group of knots. I'll give an overview of this technique and discuss some of its applications.
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Peter Feller24/05/2023, 09:30
Pete (in an informal seminar) and before him Livingston wondered, whether there exist non-isotopic oriented surfaces in the 3-sphere with boundary a fixed knot that remain non-isotopic when pushed into the 4-ball. It turns out that such examples exist, as recently observed by Hayden-Kim-Miller-Park-Sundberg, and, surprisingly, they can be distinguished by a classical invariant: the...
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Claudia Scheimbauer (University of Munich)24/05/2023, 10:45
Vector spaces having “duals” are automatically finite dimensional, and this is the case for those appearing as values of TFTs. However, if we assume that the vector spaces are pointed, they are automatically one dimensional (lines). When constructing extended n-dimensional TFTs, a natural family of targets (replaceing Vect) naturally has the feature that pointings are built in. This is due to...
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André Henriques24/05/2023, 11:35
I will present a conjecture according to which the 0-1 part of an extended 2d QFTs is, up to isomorphism, independent of the QFT.
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This conjecture is analogous to the well known fact that there exists a unique separable Hilbert space up to isomorphism (a Hilbert space is the 0 part of a 1d QFT), and has striking consequences about the existence of various kinds of symmetries. -
Michael Freedman24/05/2023, 21:00
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Sergei Gukov25/05/2023, 09:30
Considering the special occasion and to diversify the list of topics, in this talk, intended for a broad audience, I decided to turn to something that hopefully can be fun and entertaining: While the "state-of-the-art" machine learning algorithms already make an impact at the level of high school or undergraduate curriculum, in this talk I want to explore whether they can help us with some of...
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Nathalie Wahl25/05/2023, 10:45
String topology can be seen as a form of 2d field theory on the homology of the free loop spaces of manifolds. I’ll describe this field theory, and exhibit some of its interesting features.
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Slava Krushkal25/05/2023, 11:35
I will discuss work in progress, joint with Sergei Gukov, Lennart Meier, and Du Pei. It concerns a construction of a 4-manifold invariant using the theory of topological modular forms, and TQFT properties of this invariant. This is a mathematical construction related to a particular instance of the Gukov-Pei-Putrov-Vafa program associating an invariant of 4-manifolds to certain 6-dimensional...
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James Conant (Gemological Institute of America)25/05/2023, 14:00
In the first part of the talk, we give some background on the geometry of diamond cuts, and the special optical properties that make them so captivating to look at. In the second part, we discuss how the classical mathematics of the Maxwell-Cremona correspondence can assist in the enumeration of possible diamond cuts.
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Grigori Avramidi26/05/2023, 09:30
A basic problem in low dimensional topology is to understand the 2-complexes with a given fundamental group G. I will explain how this can be studied using a division algorithm in the group ring of G, and describe some instances in which such an algorithm is available.
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Luciana Basualdo Bonatto (MPIM)26/05/2023, 10:45
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A graph $G$ is maximal knotless if it is edge maximal for the property of having a knotless embedding. That is, there exists an embedding of $G$ into $S^3$ such that every cycle in $G$ is the unknot, but for any edge $e$, any embedding of $G’ = G + e$ has a cycle that is embedded as a non-trivial knot.
We show that any maximal knotless graph must have at least $|E| \geq \frac{7}{4}|V|$...
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Understanding moduli spaces of manifolds has been closely related to understanding (invertible) topological field theories, through the classifying space of the cobordism category. Inspired by generalized categories of cobordisms where manifolds can have punctures or singularities, and by factorization homology, we look at a generalized moduli space construction. These can be modelled as...
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In 4-dimensional topology, differences between the smooth and topological categories can be understood as a failure of smoothing topologically embedded disks. Modern smooth techniques, including these from gauge theory, detect a large extent of the failure of disk smoothing, but little was known about when topological disks are smoothable. I will talk about a new smoothing technique for...
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Dmitri Pavlov
I will explain my recent work with Daniel Grady on locality of functorial field theories (arXiv:2011.01208) and the geometric cobordism hypothesis (arXiv:2111.01095). The latter generalizes the Baez–Dolan cobordism hypothesis to nontopological field theories, in which bordisms can be equipped with geometric structures, such as smooth maps to a fixed target manifold, Riemannian metrics,...
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We outline a construction of the spinor bundle of the loop space of a string manifold together with its fusion product. This construction was outlined by Stolz and Teichner in a preprint from 2005. In particular, we prove that the loop space of an oriented manifold X admits a spinor bundle with a fusion product if and only if X is string. Our work partially extends and somewhat simplifies a...
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The stringor bundle has been anticipated by pioneering work of Stephan Stolz and Peter Teichner, as a string-theoretic analog of the spinor bundle of quantum mechanics. In this talk, I will explain a neat construction of the stringor bundle as an associated 2-vector bundle. The main ingeredients are a new model for the string 2-group and a representation of that 2-group on a von Neumann algebra.
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Dan Freed
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