Every semester, a group of GW topologists and their friends organize an international conference on Knot Theory and its Ramifications in or near Washington, DC. This tradition was started in the fall of 1995 by Jozef H. Przytycki and Yongwu Rong on the heels of a very successful first Knots in Poland conference organized in Warsaw by Joanna Kania-Bartoszynska, Jozef H. Przytycki and Pawel Traczyk.

The masterclass will present spectacular recent advances in motivic filtrations and their applications. To briefly put this in context, every cohomology theory, in arithmetic geometry and elsewhere, should arise as the graded pieces of a motivic filtration of some localizing invariant, algebraic K-theory and topological cyclic homology being notable examples. The definition of the appropriate motivic filtrations, however, was long elusive. Voevodsky received the 2002 Fields medal, in part, for his definition of the motivic filtration of algebraic K-theory of schemes smooth over a field. This definition, however, was based on algebraic cycles, which are notoriously difficult to handle. In 2018, Bhatt, Morrow, and Scholze defined a motivic filtration of p-complete topological cyclic homology in an entirely different way, which is much simpler and easier to employ elsewhere, and this breakthrough has led to numerous advances.

Building on work of Antieau, Morin, and, independently, Bhatt-Lurie, have refined the Bhatt-Morrow-Scholze filtration to a filtration of non-completed topological cyclic homology, and Morin discovered that its graded pieces precisely account for an archimedean factor in a conjectural formula for the special values of the Hasse-Weil zeta function of a regular scheme, proper over the integers. It is very exciting to see that such quantative archimedean information can be extracted from topological cyclic homology! More recently, Hahn-Raksit-Wilson introduced the even filtration, and showed that it accounts for both the Bhatt-Morrow-Scholze filtration and the Morin and Bhatt-Lurie refinements thereof. It might also recover and extend Voevodsky's filtration?

The main scientific theme of the workshop is counting BPS states in physical systems associated to 3-manifolds or links, and interpretation of these counts as old or new topological invariants.

Although the ideas behind such relations appeared already in the late 90s, the recent years have seen some dramatic new developments. The goal of this learning workshop is to bring together physicists and mathematicians who are experts in the subject and also those who would like to enter the field. In particular, the talks will be given both by senior scientists and junior ones, including PhD students who only recently began working on the subject. The talks will be supplemented by dedicated discussion sessions where experts can answer questions that will be submitted by participants to the moderator in advance, or asked directly during the session.

Topics:

-- "Z-hat" and F_K invariants counting BPS states in 6d superconformal field theory compactified on 3- manifolds, and their relation to known invariants of 3-manifolds and links

-- Knots-quivers correspondence and its generalization to knot complements

-- Properties of generating functions counting BPS states, including: modularity, relation to characters of (logarithmic) Vertex Operator Algebras, GW/DT invariants

There is a history of fruitful links between low-dimensional topology and number theory, going back at least to Mazur's observation that primes in number rings can be viewed as analogues of knots in a 3-manifold. More recently, the introduction of arithmetic gauge theory by M. Kim and collaborators paves the way to further bring ideas from theoretical physics to bear on fundamental problems in number theory and arithmetic geometry. 

This conference aims to explore this exciting new direction, and the links between number theory, topology and physics in general, with a particular focus on the role played by gauge fields as a unifying framework. In doing this, we will bring together experts and early career researchers in each of the areas mentioned above, with a view to fostering new collaborations and enabling participants to become acquainted with recent developments.

A conference on Homotopy theory at Northwestern to honor the contributions of Paul Goerss.

A Conference in Honour of Mike Hopkins

The 2023 Summer School on Scissors Congruence, Algebraic K-theory, and Trace Methods for graduate students and early career researchers will be held June 26-30 at Indiana University, Bloomington.

The summer school will include mini-courses on:

• Algebraic K-theory - Mona Merling
• Scissors congruence K-theory - Inna Zakharevich
• Trace methods - Teena Gerhardt and Cary Malkiewich

The summer school will also feature problem sessions and student talks on foundational papers in the area.

We expect to provide housing for invited participants as well as (partial) reimbursement for travel expenses. We expect approximately 40-50 participants overall.

For more information, and to apply, please see: https://topology.math.indiana.edu/Summer2023/
Applications are due January 31st, 2023.

Organizing Committee:

• Andrew Blumberg
• Teena Gerhardt
• Michael Hill
• Cary Malkiewich
• Michael Mandell

• Andrew Blumberg, Columbia University
• Anna Marie Bohmann, Vanderbilt University
• Teena Gerhardt, Michigan State University
• Mike Hill, UCLA
• Cary Malkiewich, Binghamton University
• Michael Mandell, Indiana University
• Mona Merling, University of Pennsylvania
• Kate Ponto, University of Kentucky
• Inna Zakharevich, Cornell University

The Department of Mathematics of University of Patras and the Department of Electrical and Computer Engineering of University of Peloponnese with the hospitality of the city of Nafpaktos organize the:

"2023 International Conference on Topology and its Applications, July 3-7, 2023, Nafpaktos, Greece"

Organizing Committee: S. Iliadis - Chairman, D. Georgiou (Department of Mathematics, University of Patras, Patra, Greece), I. Kougias (Department of Electrical and Computer Engineering, University of Peloponnese, Patra, Greece), A. Megaritis (Department of Physics, University of Thessaly, Lamia, Greece), F. Sereti (Department of Mathematics, University of Western Macedonia, Kastoria, Greece), V. Gkizas (Mayor of the Municipality of Nafpaktia)

Host:
University of Patras - University of Peloponnese

Homepage:: http://www.lepantotopology.gr

e-mail: [email protected]

Description: All areas of Topology and its Applications are included: General Topology, Set-Theoretic Topology, Geometric Topology, Algebraic Topology, Applied Topology. In particular: Topological Groups, Dimension Theory, Dynamical Systems and Continua Theory, Computational Topology, History of Topology.

The above conference is the continuation of the following conferences:

(1) 2006 International Conference on Topology and its Applications,_ June 23-26, 2006, Aegion, Greece.

(2) 2010 International Conference on Topology and its Applications,_ June 26-30, 2010, Nafpaktos, Greece.

(3) 2014 International Conference on Topology and its Applications,_ June 3-7, 2014, Nafpaktos, Greece.

(4) 2018 International Conference on Topology and its Applications,_ July 3-7, 2018, Nafpaktos, Greece.

This conference is organized around the themes of K-theory, (motivic) homotopy theory, topological Hochschild homology, trace methods, and related topics. It is dedicated to Bjørn Ian Dundas on the occasion of his 60th birthday.

Victor P. Snaith (1944 – 2021) was distinguished not just as an outstanding mathematician who made deep and lasting contributions in algebraic topology and number theory but also as a charismatic leader who enthusiastically developed research communities and generously supported young researchers.

The conference will bring together homotopy theory, cohomology of groups, algebraic K-theory and number theory, the main areas in which Vic worked. The aim is to feature important developments, paying special attention to synergies between these areas, as Vic did in much of his versatile research.

See conference website