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17:00 -- 18:00 Online seminar on Zoom.

Information :@

Kazuo Habiro

Nariya Kawazumi

Takahiro Kitayama

Takuya Sakasai

Pre-registration is required.

Once you register, you can attend all our seminars until the end of March, 2024.

The zoom meeting will be opened 15 minutes before start.

Making audio and video recordings is prohibited.

April 9, 17:00-18:30 -- Room 056 with live streaming on Zoom

Shouhei Honda (The University of Tokyo)

Abstract: Gromov-Hausdorff distance defines a distance on the set of all isometry classes of compact metric spaces. It is natural to ask about topological relationships between two compact metric spaces whose Gromov-Hausdorff distance is small. Cheeger-Colding provided a striking result about this question, under a (lower) curvature bound on Ricci curvature. In this talk we will improve this result sharply. This is a joint work with Yuanlin Peng (Tohoku University). If time permits, along this direction, we will also discuss a recent work about a topological stability result to flat tori via harmonic maps, where this is a joint work with Christian Ketterer (University of Freiburg), Ilaria Mondello (Université de Paris Est Créteil), Chiara Rigoni (University of Vienna) and Raquel Perales (CIMAT).

April 16, 17:00-18:30 -- Online on Zoom

Hiroaki Karuo (Gakushuin University)

Abstract: To understand the algebraic structures of skein algebras and their generalizations, we usually try to embed these algebras into quantum tori using ideal triangulations of a surface and the splitting map. However, such a construction does not work for the skein algebras of closed surfaces and the Roger-Yang skein algebras of punctured surfaces.

In the talk, we define filtrations on these algebras using pants decompositions and embed the associated graded algebras into quantum tori. As a consequence, Roger-Yang skein algebras are quantizations of decorated Teichmuller spaces. This talk is based on a joint work with Wade Bloomquist (Morningside University) and Thang Le (Georgia Institute of Technology).

April 23, 17:00-18:30 -- Room 056 with live streaming on Zoom

Tatsumasa Suzuki (Meiji University)

Abstract: This talk consists of the following two research contents:

I. The boundary sum of S

II. In 2003, Peter Ozsváth and Zoltán Szabó introduced a homology cobordism invariant for homology 3-spheres called a d-invariant. In this talk, we present new computable examples by refining the Karakurt--Şavk formula for any Brieskorn homology 3-sphere ∑(p,q,r) with p is odd and pq+pr-qr=1. Furthermore, by refining the Can-Karakurt formula for the d-invariant of any ∑(p,q,r), we also introduce the relationship with the d-invariant of ∑(p,q,r) and those of lens spaces. This talk includes contents of joint work with Motoo Tange (University of Tsukuba).

May 7, 17:00-18:00 -- Online on Zoom

Ingrid Irmer (Southern University of Science and Technology)

Abstract: The systole function f

May 14, 17:00-18:00 -- Online on Zoom

Noriyuki Hamada (Institute of Mathematics for Industry, Kyushu University)

Abstract: We will talk about our novel examples of symplectic 4-manifolds, which are homeomorphic but not diffeomorphic to the standard simply-connected closed 4-manifolds with signature zero. In particular, they provide such examples with the smallest Euler characteristics known to date. Our method employs the time-honored approach of reverse-engineering, while the key new ingredients are the model manifolds that we build from scratch as Lefschetz fibrations. Notably, our method greatly simplifies pi_1 calculations, typically the most intricate aspect in existing literature. This is joint work with Inanc Baykur (University of Massachusetts Amherst).

May 21, 17:30-18:30 -- Room 056 with live streaming on Zoom

Yuichi Ike (Institute of Mathematics for Industry, Kyushu University)

Abstract: The space of smooth compact exact Lagrangians of a cotangent bundle carries the spectral metric γ, and we consider its completion. With an element of the completion, Viterbo associated a closed subset called γ-support. In this talk, I will explain how we can use sheaf-theoretic methods to explore the completion and γ-supports. I will show that we can associate a sheaf with an element of the completion, and its (reduced) microsupport is equal to the γ-support through the correspondence. With this equality, I will also show several properties of γ-supports. This is joint work with Tomohiro Asano (RIMS), Stéphane Guillermou (Nantes Université), Vincent Humilière (Sorbonne Université), and Claude Viterbo (Université Paris-Saclay).

May 28, 17:00-18:00 -- Online on Zoom

Andreani Petrou (Okinawa Institute of Science and Technology)

Abstract: The Harer-Zagier (HZ) transform is a discrete Laplace transform that can be applied to knot polynomials, mapping them into a rational function of two variables λ and q. The HZ transform of the HOMFLY-PT polynomial has a simple form, as it can be written as a sum of factorised terms. For some special families of knots, it can be fully factorised and it is completely determined by a set of exponents. There is an interesting relation between such exponents and Khovanov homology. Moreover, we conjecture that there is an 1-1 correspondence with such factorisability and a relation between the HOMFLY-PT and Kauffman polynomials. Furthermore, we suggest that by fixing the variable λ = q

June 4, 17:00-18:00 -- Online on Zoom

Katsumi Ishikawa (RIMS, Kyoto University)

Abstract: The trapezoidal conjecture is a classical famous conjecture posed by Fox, which states that the coefficient sequence of the Alexander polynomial of any alternating link is trapezoidal. In this talk, we show this conjecture for any alternating links of braid index 3. Although the result holds for any choice of the orientation, we shall mainly discuss the case of the closures of alternating 3-braids with parallel orientations.

June 11, 17:00-18:30 -- Room 056 with live streaming on Zoom

Nariya Kawazumi (The University of Tokyo)

Abstract: Wolpert explicitly described the Weil-Petersson symplectic form on the Teichmüller space in terms of the Fenchel-Nielsen coordinate system, which comes from a pants decomposition of a surface. By introducing a natural cell-decomposition associated with the decomposition, we give a topological proof of Wolpert's formula, where the symplectic form localizes near the simple closed curves defining the decomposition.

June 20 (Thu) [Joint with RIKEN iTHEMS], 17:00-18:30 -- Room 002 with live streaming on Zoom

Dominik Inauen (University of Leipzig)

Abstract: The problem of embedding abstract Riemannian manifolds isometrically (i.e. preserving the lengths) into Euclidean space stems from the conceptually fundamental question of whether abstract Riemannian manifolds and submanifolds of Euclidean space are the same. As it turns out, such embeddings have a drastically different behaviour at low regularity (i.e. C

June 25 [Joint with RIKEN iTHEMS], 17:00-18:30 -- Room 056 with live streaming on Zoom

Emmy Murphy (University of Toronto)

Abstract: Even though C