Events

OIST's Visiting Program (TSVP)

Events

Seminar

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

2026-09-16

L5D23 and zoom

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

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

2026-09-16

L5D23 and zoom

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.

Recreation

Coffee Hour at the Visiting Program

2026-09-28

L5EF03

"Visiting Program Coffee Hour": informal discussions and getting to know each other, in the Visiting Program (TSVP) area in Lab 5 EF03

Lecture

TSVP Talk: Why “Science education and public engagement” – and why at OIST?

2026-10-01

C700 and zoom

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).