Title: Designing Complex Fluids: Leveraging Rheology for Advanced Manufacturing

Speaker: Dr. Chaimongkol Saengow, Lecturer, the Sirindhorn International Institute of Technology, Thammasat University

This seminar is co-hosted by the Mechanics and Materials Unit and the Micro/Bio/Nanofluidics Unit

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.

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.

Language: English

Seminar by Dr. Jihong Zhu on September 16, 2026, 13:00-14:00 in L4E01

Professor Matthew Middleton, Director of the Southampton Space Institute Deputy Head of School (Education), School of Physics and Astronomy University of Southampton

The seminar will focus on risk management, with invited external experts discussing risk management in research laboratories and across the university as a whole.

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).

Latest research on the Darwinian evolution of RNA-protein self-replication systems, synthetic gene circuits, and mirror-image biology. 

Prof. Myung-Gil Kim, School of Advanced Materials Science & Engineering, Sungkyunkwan University