Scientific Organiser(s):
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Dohyeong Kim, Seoul National University
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Masanori Morishita, Kyushu University
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Adam Morgan, University of Glasgow
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Amina Abdurrahman, IHES
About:
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 aimed 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 brought 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.
Programme:
| Monday 6 March | ||
| Registration and Refreshments | ||
| Welcome and Housekeeping | ||
| Nadav Gropper, Ben-Gurion University of the Negev | Surfaces and p-adic fields | |
| Rajath Radhakrishnan, International Centre for Theoretical Physics | Integral Combinations of Characters from 2D TQFTs | |
| Tynan Ochse, University of Texas at Austin | Towards arithmetic Floer cohomology | |
| Lunch | ||
| Jonathan Pridham, University of Edinburgh | Derived analytic moduli of Galois representations with shifted symplectic structures | |
| Refreshments | ||
| Sergei Gukov, DIAS / Caltech | 3d Modularity Conjecture | |
| Welcome Reception, hosted at ICMS | ||
| Tuesday 7 March | ||
| Oren Ben-Bassat, University of Haifa | Banach Algebraic Geometry | |
| Refreshments | ||
| Jack Kelly, Trinity College Dublin | Bornological Spectra and Bounded Cohomology | |
| Ryoto Tange, Waseda University | L-invariants for representations of knot groups | |
| Toshiki Matsusaka, Kyushu University | Hikami’s observations on unified WRT invariants and false theta functions | |
| Lunch | ||
| Hiroaki Karuo, Gakushuin University | The reduced Dijkgraaf--Witten invariant of knots in the Bloch group of a finite field | |
| Refreshments | ||
| Fernando Rodriguez Villegas, ICTP | Character varieties for unitary groups | |
| Wednesday 8 March | ||
| Jeehoon Park, QSMS / Seoul National University | The Cassels-Tate pairings and the arithmetic BF theory for Selmer groups | |
| Refreshments | ||
| Jun Ueki, Ochanomizu University | p-adic torsion growth in p-adic towers | |
| Jay Swar, University of Oxford | Symplectic structures on Selmer schemes | |
| Tony Pantev, University of Pennsylvania | Enhanced moduli of D-branes and superpotentials | |
| Lunch | ||
| Thursday 9 March | ||
| Amina Abdurrahman, IHES | Square roots of symplectic L-functions and Reidemeister torsion | |
| Refreshments | ||
| Akihito Mori, Tohoku University | Relations between Reshetikhin--Turaev and re-normalized link invariants | |
| Wataru Kai, Tohoku University / University of Milan | The Green-Tao theorem for number fields (and beyond) | |
| Masanori Morishita, Kyushu University | Symbols on 3-manifolds and conformal field theory | |
| Lunch | ||
| Magnus Carlson, Stockholm University | Massey products in étale cohomology | |
| Refreshments | ||
| Yuya Murakami, Tohoku University | A proof of a conjecture by Gukov-Pei-Putrov-Vafa | |
| Workshop Dinner, hosted at Blonde Restaurant | ||
| Friday 10 March | ||
| Christopher Deninger, University of Münster | Dynamical systems for arithmetic schemes | |
| Refreshments | ||
| Yifei Zhao, University of Münster | Langlands parametrization for covering groups | |
| End of Workshop |
