A proof of N. Takahashi’s conjecture for (P2,E) and a refined sheaves/Gromov–Witten correspondence
Bousseau, P Duke Mathematical Journal volume 172 issue 15 2895-2955 (15 Oct 2023) doi:10.1215/00127094-2022-0095
BPS dendroscopy on local P2
Bousseau, P Descombes, P Le Floch, B Pioline, B Communications in Mathematical Physics volume 405 issue 4 (16 Apr 2024) doi:10.1007/s00220-024-04938-3
Strong positivity for the skein algebras of the 4-punctured sphere and of the 1-punctured torus
Bousseau, P Communications in Mathematical Physics volume 398 issue 1 1-58 (19 Nov 2022) doi:10.1007/s00220-022-04512-9
On the log–local principle for the toric boundary
Bousseau, P Brini, A van Garrel, M Bulletin of the London Mathematical Society volume 54 issue 1 161-181 (07 Feb 2022) doi:10.1112/blms.12566
Computational Synthesis of Cortical Dendritic Morphologies
Kanari, L Dictus, H Chalimourda, A Van Geit, W Coste, B Shillcock, J Hess, K Markram, H (2020) doi:10.2139/ssrn.3596620
Modeling and Simulation of Neocortical Micro- and Mesocircuitry. Part I: Anatomy
Reimann, M Bolaños-Puchet, S Courcol, J Egas Santander, D Arnaudon, A Coste, B Delalondre, F Delemontex, T Devresse, A Dictus, H Dietz, A Ecker, A Favreau, C Ficarelli, G Gevaert, M Herttuainen, J Isbister, J Kanari, L Keller, D King, J Kumbhar, P Lapere, S Lazovskis, J Lu, H Ninin, N Pereira, F Planas, J Pokorny, C Riquelme, J Romani, A Shi, Y Smith, J Sood, V Srivastava, M Van Geit, W Vanherpe, L Wolf, M Levi, R Hess, K Schürmann, F Muller, E Markram, H Ramaswamy, S (26 Nov 2024) doi:10.7554/elife.99688.2
Community-based Reconstruction and Simulation of a Full-scale Model of Region CA1 of Rat Hippocampus
Romani, A Antonietti, A Bella, D Budd, J Giacalone, E Kurban, K Sáray, S Abdellah, M Arnaudon, A Boci, E Colangelo, C Courcol, J Delemontex, T Ecker, A Falck, J Favreau, C Gevaert, M Hernando, J Herttuainen, J Ivaska, G Kanari, L Kaufmann, A King, J Kumbhar, P Lange, S Lu, H Lupascu, C Migliore, R Petitjean, F Planas, J Rai, P Ramaswamy, S Reimann, M Riquelme, J Guerrero, N Shi, Y Sood, V Sy, M Van Geit, W Vanherpe, L Freund, T Mercer, A Muller, E Schürmann, F Thomson, A Migliore, M Káli, S Markram, H (2023) doi:10.1101/2023.05.17.541167
Multihumped collapsing solutions in the nonlinear Schrödinger problem: existence, stability, and dynamics
Chapman, J Kavousanakis, M Charalampidis, E Kevrekidis, I Kevrekidis, P SIAM Journal on Applied Dynamical Systems volume 25 issue 2 654-694 (02 Apr 2026) doi:10.1137/25m1755576
Thu, 27 Nov 2025
11:00

Incidence Bounds in Valued Fields with Finite Residue Field

Mira Tartarotti
Abstract

Elekes and Szabó established non-trivial incidence bounds for binary algebraic relations in characteristic 0, generalizing the Szemerédi-Trotter theorem for point-line-incidence. This was later generalized to binary relations defined in reducts of so-called distal structures in a result of Chernikov, Peterzil and Starchenko. For fields of positive characteristic, such bounds fail to hold in general. Bays and Martin apply the bounds for distal structures in the context of valued fields to derive incidence bounds in the sense of Szemerédi-Trotter in fields admitting valuations with finite residue field, such as F_p(t). We show that this result can be made uniform in the size of the finite residue field, by making precise in some sense the intuition that ACVF is distal relative to the residue field. In this talk, I will introduce the relevant notions from incidence combinatorics and distality, before outlining a proof of the uniform-in-p result.

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