Motives, mapping class groups, and monodromy in Lanzarote

February 24th - 28th

Hotel Costa Calero Thalasso & Spa

Organized by Greg Baldi and Javier Fresán

Scientific program: Greg Baldi, Javier Fresán, Josh Lam, Aaron Landesman, Daniel Litt

Generously sponsored by Baldi’s ANR-HoLoDiRibey of the Agence Nationale de la Recherche.

Participants

  • Yves André
  • Greg Baldi
  • Paul Brommer-Wierig
  • Anna Cadoret
  • Javier Fresán
  • Franco Giovenzana
  • Giada Grossi
  • Peter Jossen
  • Bruno Klingler
  • Jef Laga
  • Josh Lam
  • Aaron Landesman
  • Carlos Matheus
  • Yilin Ni
  • Ania Otwinowska
  • Federico Scavia
  • David Urbanik
Time Monday Tuesday Wednesday Thursday Friday
10:00-11:00 Talk 1 Talk 5 Talk 9 Talk 11 Talk 15
11:30-12:30 Talk 2 Talk 6 Talk 10 Talk 12 Talk 16
12:30-14:30 Lunch Break
14:30-15:30 Talk 3 Talk 7 Free afternoon Talk 13 Talk 17
16:00-17:00 Talk 4 Talk 8 - Talk 14 Q&A Session
17:00-18:00 - Q&A Session - - -
19:00 Onwards Dinner Dinner Dinner Dinner Dinner

Talk-by-Talk Program

Day 1

  • Talk 1: Introduction/overview of the main topics. Local systems on curves and MCG-finiteness, isomonodromy, braid groups. [L24]
  • Talk 2: Isomonodromic Deformations, Painlevé VI and their algebraic solutions.
  • Talk 3: A survey of non-abelian Hodge theory.
  • Talk 4: Motivic and rigid local systems. The middle convolution algorithm [K].

Day 2

  • Talk 5: Beauville’s work [B], and geometric local systems on the projective line minus four points [LL23b].
  • Talk 6: Work of Esnault-Groechenig [EG18] on cohomologically rigid local systems.
  • Talk 7: Work of Corlette and Simpson [CS].
  • Talk 8: Étale local systems, relative Fontaine--Mazur, after Liu--Zhu [LZ], Petrov [P]. Constructing abelian varieties from rank 2 Galois representations [ST, KYZ].

Day 3

  • Talk 9: Putman-Wieland conjecture [PW, LL23a].
  • Talk 10: [LL24b, Theorem 1.2.5] - statement, corollaries.

Day 4

  • Talk 11: Proof of the above theorem.
  • Talk 12: [LL24a, Theorem 1.2.1] - statement, corollaries, setting.
  • Talk 13: Proof of the above.
  • Talk 14: Introduction to [LLL23] and Theorem 1.1.2 thereof.

Day 5

  • Talk 15: Proofs from [LLL23].
  • Talk 16: p-curvature I: overview and conjecture from [LL25].
  • Talk 17: p-curvature II: linear and non-linear differential equations.

References

  • [B]: Beauville. Les familles stables de courbes elliptiques sur P^1 admettant quatre fibres singuli`eres.
  • [CS]: Corlette and Simpson. On the classification of rank two representations of quasiprojective fundamental groups
  • [EG18]: Esnault and Groechenig. Rigid connections and F-isocrystals
  • [K]: Katz. Rigid local systems
  • [KYZ]: Krishnamoorthy, Yang, and Zuo. Constructing abelian varieties from rank 2 Galois representations
  • [LL23a]: Landesman and Litt. An introduction to the algebraic geometry of the Putman-Wieland conjecture
  • [LL23b]: Lam and Litt. Geometric local systems on the projective line minus four points
  • [LLL23]: Lam, Landesman, and Litt. Finite braid group orbits on SL_2-character varieties
  • [LL24a]: Landesman and Litt. Canonical representations of surface groups
  • [LL24b]: Landesman and Litt. Geometric local systems on very general curves and isomonodromy
  • [LL25]: Lam and Litt. Algebraicity and integrality of solutions to differential equations
  • [L24]: Litt. Motives, mapping class groups, and monodromy
  • [LZ]: Liu and Zhu. Rigidity and a Riemann-Hilbert correspondence for p-adic local systems
  • [PW]: Putman and Wieland. Abelian quotients of subgroups of the mappings class group and higher Prym representations
  • [P]: Petrov. Geometrically irreducible p-adic local systems are de Rham up to a twist
  • [ST]: Snowden and Tsimerman. Constructing elliptic curves from Galois representations