Scientific organisers
-
Eric Ahlqvist , University of Edinburgh
-
Magnus Carlson , Goethe-Universität Frankfurt
-
Amina Abdurrahman , IHES
About:
As first observed by Mazur and Mumford, there exists a deep analogy between 3-manifolds and number fields. In the 90s, Morishita expanded upon and delved deeper into these connections between low-dimensional topology and number fields. More recently, Minhyong Kim proposed that, in line with the aforementioned analogy, one should develop “arithmetic field theories” for number fields. Kim’s proposal invigorated interest in this area of study, leading to a plethora of new research directions. Examples include the work of Kim and collaborators, as well as connections to the Langlands program explored by Ben-Zvi—Sakellaridis—Venkatesh. The once-unexpected comparison between 3-manifolds and number fields is now proving fruitful, and it promises to illuminate number theory, potentially leading to significant breakthroughs.
This workshop will bring together experts and young researchers to further explore a field that is still largely unexplored. While the analogies are striking, we believe that the field has not yet seen its full potential. One of the goals of the workshop is to find new problems which can be attacked with ideas stemming from the analogy between number fields and 3-manifolds.
We are grateful for the financial support from the Glasgow Mathematical Journal Learning and Research Support Fund, Foundation Compositio Mathematica, London Mathematical Society, UKRI, Heilbronn Institute for Mathematical Research and Edinburgh Mathematical Society.
Participation
No late applications and walk-in attendees will be accepted.
Please note, invited participants and speakers will receive an email directly from ICMS and should not apply on this webpage.
Scam Warning
We are aware of a number of current scams targeting participants at ICMS workshops in relation to registration or accommodation bookings. If you are approached by a third party (e.g., travellerpoint.org, Conference Committee or Royal Visit) asking for booking or payment details, these scammers may telephone or email you and tell you that they are organising accommodation in Edinburgh for you on behalf of ICMS. please ignore.
Please note:
i) ICMS never uses third parties to do our administration for events: messages will come directly from ICMS staff;
ii) ICMS never asks participants for credit card or bank details;
iii) If you have any doubts about an email you receive, please get in touch with us.
Programme:
MONDAY 15 APRIL 2024 | ||
Registration | ||
Welcome & introduction | ||
Amina Abdurrahman, IHES | ||
Coffee Break | ||
Maxim Zabzine, Uppsala University | Gauge theories, diagrammatics and algebra | |
Lunch | ||
Alison Beth Miller, University of Michigan | Disjoint Seifert surfaces and composition of binary quadratic forms | |
Coffee Break | ||
Toshiki Matsusaka, Kyushu University | Modular knots, automorphic forms, and the Rademacher symbols | |
Drinks reception | ||
TUESDAY 16 APRIL 2024 | ||
Ruth Lawrence-Naimark, Hebrew University of Jerusalem | Discrete approximations to the continuum and combinatorial transverse intersection algebra | |
Coffee Break | ||
Artane Siad, IAS | Spin structures and quadratic enhancements on number fields | |
Lunch | ||
Anna Beliakova, University of Zürich | On algebraisation of low-dimensional Topology | |
Coffee Break | ||
Eric Chen, EPFL | Relative Langlands duality and Mirror Branes | |
WEDNESDAY 17 APRIL 2024 | ||
Sherry Gong, Texas A&M University | On concordance invariants from instantons | |
Coffee Break | ||
Clark Barwick, University of Edinburgh | Factorization algebras in quite a lot of generality | |
Ariel Davis, Hebrew University of Jerusalem | Primes, Knots and Keis - Coloring Square-free Integers | |
Lunch & free afternoon | ||
THURSDAY 18 APRIL 2024 | ||
Masanori Morishita, Kyushu University | On arithmetic Chern-Simons theory and metaplectic theory | |
Coffee Break | ||
David Jordan, University of Edinburgh | Langlands duality in quantum topology | |
Lunch | ||
Jennifer Brown, University of Edinburgh | Orthogonal Quantum Invariants | |
Coffee Break | ||
Mark Shusterman, Weizmann Institute of Science | An Arithmetic Topology Analog of Hecke’s Theorem | |
Workshop dinner | ||
FRIDAY 19 APRIL 2024 | ||
Alex Bartel, University of Glasgow | Isospectral manifolds from orders in quaternion algebras | |
Coffee Break | ||
Dohyeong Kim, Seoul National University | Triple symbols in arithmetic | |
Lunch & end of the workshop |