Dynamics, Fluctuations, and Entanglement in Quantum Materials and Many-Body Systems

Dynamics, Fluctuations, and Entanglement in Quantum Materials and Many-Body Systems

[Seminar] "Universal Link Invariants via Configuration Spaces" by Cristina Ana-Maria Anghel

Cristina Ana-Maria Anghel (Université Clermont Auvergne): October 13, 4pm-5pm, lecture room L5D23 (online talk).

Title: Universal Link Invariants via Configuration Spaces

Abstract: Coloured Jones and Alexander polynomials are quantum invariants originating in representation theory and their geometric information is an important open problem in quantum topology. We present a new topological perspective that unifies these invariants through the topology of configuration spaces. First, for a fixed N, we define new link invariants: "N-th Unified Jones invariant" and "N-th Unified Alexander invariant" globalising all coloured Jones and ADO link polynomials of (multi)-colours bounded by N. Asymptotically, Habiro defined his universal knot invariant globalising coloured Jones polynomials by introducing the Habiro ring. For the link case, such globalisation remained open for both sequences of invariants. We answer this problem coming from representation theory using topological tools. On the representation theory side we define extensions of Habiro type rings. On the topological side, we construct a universal Jones link invariant and a universal Alexander link invariant. Putting these together, our universal invariants of geometrical nature take values in the extended Habiro rings that we construct. 

[Seminar] "Towards a Bogomolov-Miyaoka-Yau inequality for symplectic 4-manifolds, II" by Paul Feehan

Paul Feehan (Rutgers University): October 13, 2:30pm-3:30pm, lecture room L5D23.

Title:  Towards a Bogomolov-Miyaoka-Yau inequality for symplectic 4-manifolds, II

Abstract: The Bogomolov-Miyaoka-Yau inequality for minimal compact complex surfaces of general type was proved in 1977 independently by Miyaoka, using methods of algebraic geometry, and by Yau, as an outgrowth of his proof of the Calabi conjectures. In this talk, we describe progress in our ongoing program to prove the conjecture that symplectic 4-manifolds obey the Bogomolov-Miyaoka-Yau inequality. Our program uses Morse theory on the gauge theoretic moduli space of non-Abelian monopoles, where the Morse function is a Hamiltonian for a natural circle action and natural two-form. We shall describe generalizations of Donaldson’s symplectic subspace criterion (1996) from finite to infinite dimensions and generalizations of Taubes' perturbation analysis from the Seiberg-Witten to non-Abelian monopole equations. These methods have application to the problem of showing that the fundamental two-form is non-degenerate and thus an almost symplectic form on the moduli space of non-Abelian monopoles. This talk is based on joint work with Tom Leness and the monographs https://arxiv.org/abs/2010.15789 (to appear in AMS Mathematical Surveys and Monographs),  https://arxiv.org/abs/2206.14710  and https://arxiv.org/abs/2410.13809.

TSVP Talk: "Numerically Verified Proofs in Geometry and Beyond" by Daniel Platt

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).

Mini-Workshop on Gauge Theory and Low-Dimensional Topology

The OIST Mini-Workshop on Gauge Theory and Low-Dimensional Topology is a three-day research meeting bringing together researchers working in gauge theory and low-dimensional topology.

The workshop is held as part of the OIST program New Frontiers in Gauge Theory, Topology, and Physics.

Workshop on "Gauge Theory and Mathematical Physics"

This workshop is part of TSVP Thematic Program “New Frontiers in Gauge Theory, Topology, and Physics” (TP26GT) at Okinawa Institute of Science and Technology.

TSVP Talk: Why “Science education and public engagement” – and why at OIST? - by Liat Ben David

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).

Ryudai-OIST Joint Symposium

Ryudai-OIST Joint Symposium

This symposium brings together researchers from the University of the Ryukyus School of Medicine and OIST to share their research and explore opportunities for scientific exchange.
By fostering interactions across institutions and disciplines, the event aims to strengthen connections, encourage collaboration, and promote the development of new research partnerships. All researchers and students from the University of the Ryukyus and OIST are welcome to participate, and attendees are invited to present their work during the poster session.

[Seminar] "The Obstruction of Orientability of Real Monopole Floer Homology" by Jin Miyazawa

Title: The Obstruction of Orientability of Real Monopole Floer Homology

Abstract: The Real Seiberg-Witten theory is one of a stong tool in knot theory and surface knot theory. For example, that can detect exotic P^2-knot and Kang-Park-Taniguchi proved that any non trivial cable of figure eight knot is not slice using Real Seiberg-Witten theory. This theory is also provide interesting phenomena in index theory, since Real Seiberg-Witten theory can be seen as a "non-linear version" of Atiya's Real K-theory. For example, there is an obstruction to orient moduli space of Real Seiberg-Witten eqations on closed 4-manifolds. Recently, Bonciocat obtained a obstruction to lift the real Heegaard Floer homology from mod 2 coefficient to Z-coefficient. In this talk, we give a canonical way to obtain Z- coefficient real monopole Floer homology of double branced cover of a link in homology S^3 in the case when the obstruction vanishes. We also proved that the Bonciocat's obstruction is also obstract Z-coefficient in real monopole, however the proof is different. This is joint work with Jiakai Li.

[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.