[Seminar] "2-torsion in Instanton Homology" by Deeparaj Bhat

Title: 2-torsion in Instanton Homology

Abstract: This talk will focus on the presence of 2-torsion in a specific flavour of instanton (knot) homology introduced by Kronheimer--Mrowka. The main results are that the Poincaré homology sphere and fibered knots in 3-manifolds exhibit 2-torsion in their instanton homology. The key gauge theoretic input used in both results is a new surgery exact triangle, which relates instanton homology of three manifolds obtained by surgeries on a knot to singular instanton homology of the knot. Time permitting, we also sketch the use of sutured Floer theory in the second main result. Part of the talk is based on joint work with Zhenkun Li and Fan Ye.

[Seminar] "Signs in real monopole Floer homology" by Jiakai Li

Title: Signs in real monopole Floer homology

Abstract: 

The computation of the 3-dimensional framed real Seiberg–Witten invariant of the branched double cover of a knot K is instrumental in Miyazawa's construction of exotic P^2-knots. This invariant, known as Miyazawa's degree invariant deg(K), is the Euler characteristic χ(HMR) of framed real monopole Floer homology (HMR).  A priori deg(K) is defined only up to an overall sign, since the real Dirac operator has no complex orientation. Worse, signs associated to distinct real spin^c structures are not comparable. Resolving the latter issue is essential for developing computational techniques for real Seiberg--WItten invariants.

I will explain how to fix the sign of the 3-dimensional count, in other words, define an absolute mod-two grading, via a mod-two index-theoretic correction term. This yields a total Euler characteristic \tilde{χ} that sums over all real spin^c structures, the analogue of \hat{χ} in real Heegaard Floer homology (HFR). Recent work of Srivastava provides the motivating results: an absolute mod-two grading in \hat{HFR} and the evaluation of \hat{χ} in terms of the Alexander polynomial at \sqrt{-1}. This is joint work with Ciprian Manolescu.

[Seminar] "Peg problems and symplectic geometry" by Andrew Lobb

Title: Peg problems and symplectic geometry.

Abstract: The unsolved Toeplitz Square Peg Problem was posed in 1911.  It asks whether all Jordan curves (subsets of the real plane homeomorphic to a circle) contain four points at the vertices of a square. We shall discuss this problem and related "peg" problems.  They sometimes admit a description in terms of symplectic geometry.
No prior knowledge of pegs or of symplectic geometry assumed.  (Joint work with Josh Greene).

Public Lecture: "数も式もない計算" by 時枝正

Title: 数も式もない計算

概要：

人——プロの数学者も含めて——は「計算」というと数や式の操作を連想しがちです。

おしなべて「数学」というと定義がはっきりした形式だ、と思い込みます。しかし人の知能は、形式の外、定義以前、数も式もない場で計算を始められるのがその本質なのです。それを手品でご説明しましょう。子どもにも楽しめ、立派な研究者にもふしぎな手品で。

略歴：

日本で生まれ、画家の卵として育ち、フランスで古典語学者になり、ちょっぴり配管工として働き、オックスフォードで数学へ転向、プリンストンで純粋数学の学位を得た後、世界を巡り応用数学・物理に携わる。

元英ケンブリッヂ、現米スタンフォード大学教授。African Institute for Mathematical Sciences (AIMS)、YouTube チャネル Numberphile などを基点に啓発活動にも忙し

言語: 日本語

Public Lecture: A World From a Sheet of Paper by Tadashi Tokieda

Public Lecture: A world from a sheet of paper

Open to all interested in the topic!
OISTにて開催される  Tadashi Tokieda 氏による公開講演に、ぜひご参加ください。

Workshop on "Gauge Theory, Topology, and Physics" (TSVP-TP26GT)

Motivated by physics, Gauge theory has a long history of spectacular applications in mathematics. Recent years have seen a number of new breakthroughs deepening the connection between mathematics and physics. This workshop aims to bring together leading researchers to speak about the latest topics in this field.

This Autumn School is part of TSVP Thematic Program “New Frontiers in Gauge Theory, Topology, and Physics” (TP26GT)
*OIST members and visiting students/researchers are welcome to attend all scientific sessions without registration.

Workshop: "Women in Gauge Theory" (TSVP-TP26GT)

This one-day workshop will be held during the same week as the Autumn School and will feature talks by leading women researchers. It will bring together experts from a broad range of research areas in Geometry, Topology, and Mathematical Physics.

This Autumn School is part of TSVP Thematic Program “New Frontiers in Gauge Theory, Topology, and Physics” (TP26GT)
*OIST members and visiting students/researchers are welcome to attend all scientific sessions without registration.

Public Lecture: "3-Manifolds and Langlands Duality" by Tasuki Kinjo

Public Lecture: "3-Manifolds and Langlands Duality" by Tasuki Kinjo (RIMS, Kyoto University)

Open to all interested in the topic!
OISTにて開催される Tasuki Kinjo 氏による公開講演に、ぜひご参加ください。

TSVP Talk: "Understanding How Fungi See Light" by Tom Richards

TSVP Talk
Language: English (no interpretation).
Target audience: General audience / everyone at OIST and beyond.
Freely accessible to all OIST members and guests without registration (also via Zoom).

Autumn School on "Gauge Theory, Topology, and Physics" (TSVP-TP26GT)

This Autumn School is part of TSVP Thematic Program “New Frontiers in Gauge Theory, Topology, and Physics” (TP26GT)

*OIST members and visiting students/researchers are welcome to attend all scientific sessions without registration.