Periods in Number Theory, Algebraic Geometry and Physics - Trimester Program

Hausdorff Center for Mathematics via YouTube

Start learning Write review

Details

Start learning

Provider

YouTube
Pricing

Free Video
Languages

English
Duration & workload

3 days 2 hours 31 minutes
Sessions

On-Demand
Level

Advanced

Found in

Explore advanced mathematical concepts through this comprehensive lecture series from the Hausdorff Research Institute for Mathematics' trimester program on periods in number theory, algebraic geometry, and physics. Delve into cutting-edge research presented by leading mathematicians covering motivic Galois groups, multiple zeta values, Feynman integrals, modular forms, and hypergeometric functions. Learn about the deep connections between algebraic geometry and mathematical physics through topics such as string amplitudes, quantum field theory, and mirror symmetry. Examine specialized areas including Chow motives, polylogarithms, elliptic curves, and automorphic forms while gaining insights into computational methods for hypergeometric equations and special values of L-functions. Discover the latest developments in motivic periods, Galois symbols, and the arithmetic properties of various mathematical structures. Access expert presentations on cluster algebras, Hodge theory, and the geometric interpretation of mathematical objects ranging from modular curves to Fermat varieties. Benefit from discussions on both theoretical foundations and practical computational approaches in modern algebraic geometry and number theory research.

Syllabus

Yves André: What is… a motivic Galois group
Leila Schneps: What is... an associator
Joseph Ayoub: The conservativity conjecture for Chow motives in characteristic zero
Yves André: Periods of relative 1 motives
Sinan Unver: Infinitesimal Chow Dilogarithm
Daniil Rudenko: Polylogarithms, cluster algebras and Zagier conjecture
Matt Kerr: Apery extensions
Richard Hain: Modular inverters
Nils Matthes: Elliptic analogs of multiple zeta values
Dinakar Ramakrishnan: What are... Galois symbols on ExE ? (E an elliptic curve)
Steven Charlton: Motivic MZV's and the cyclic insertion conjecture
Spencer Bloch: Periods and regulators
Francis Brown: Motivic periods applications
Francis Brown: A guide to motivic periods
Koji Tasaka: Totally odd multiple zeta values and period polynomials
Steven Charlton: Bowman Bradley type relations for symmetrized multiple zeta values
Henrik Bachmann: Multiple harmonic q-series at roots of unity and finite [...]
Richard Hain: What is... relative completion?
Marc Levine: Chow Witt groups, ramification and quadratic forms
Minoru Hirose: Iterated integrals and symmetrized multiple zeta values
Nobuo Sato: A conjectural generalization of Zagier's formula for zeta (2,...,2,3,2,...,2)
Stephen Lichtenbaum: Cohomological description of special values of zeta functions
Tomohide Terasoma: Period integrals of open Fermat surfaces and special values of hypergeometric
Dirk Kreimer: Amplitudes: a few conundrums
Vyacheslav P. Spiridonov: 6j-symbols for SL(2,C) group and Feynman diagrams6j-symbols for SL(2,C)
Johannes Bluemlein: Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
Stephan Stieberger: Single Valued Multiple Zeta Values and String Amplitudes
Oliver Schlotterer: Moduli space integrals in string tree level amplitudes
Pierre Vanhove: Feynman integrals and Mirror symmetry
Lance J. Dixon: Cosmic Galois Theory and Amplitudes in N=4 Super Yang Mills Theory
Francis Brown: Modular graph functions and non holomorphic modular forms
Federico Zerbini: Elliptic multiple zeta values and string amplitudes
Claude Duhr: Elliptic polylogarithms evaluated at torsion points and iterated integrals
Ralph Kaufmann: Graph Hopf algebras and their framework
Oliver Schnetz: Graphical hyperlogarithms
Erik Panzer: Multiple zeta values in deformation quantization
Werner Nahm: Quantum fields as derivatives
Guangyu Zhu: The Galois group of the category of mixed Hodge Tate structures
Richard Hain: Multiple modular motives II
Francis Brown: Multiple modular motives I
Javier Fresan: What is… an exponential period
Nils Matthes: Rational associator in small depths
Rob de Jeu: Tessellations, Bloch groups, homology group
Benjamin Enriquez: A Betti counterpart of the harmonic coproduct II
Anthony Scholl and Jan Nekovar: Plectic cohomology
Francesco Lemma: Algebraic cycles and residues of degree eight L functions of GSp4xGL2
Nobuo Sato: Charlton's conjecture on multiple zeta values
Neil Dummigan: Automorphic forms on Feit's Hermitian lattices
Michael Hoffman: Multiple zeta values and alternating MZVs arising from a combinatorial problem
Minoru Hirose: Confluence relations of multiple zeta values
Robert Kucharczyk: The geometry and arithmetic of triangular modular curves
Johannes Brödel: From elliptic multiple zeta values to modular graph functions
Christian Bogner: The analytic continuation of the kite and the sunrise integral
Bartosz Naskręcki: Elliptic and hyperelliptic realisations of low degree hypergeometric motives
Henri Cohen: Computing multiple polylogarithms after Akhilesh
Jan Stienstra: Zhegalkin Zebra Motives, digital recordings of Mirror Symmetry
Frits Beukers: Some supercongruences of arbitrary length
Wadim Zudilin: A q-microscope for hypergeometric congruences
Roberto Villaflor Loyola: Periods of linear algebraic cycles in Fermat varieties
Kiran S. Kedlaya: Frobenius structures on hypergeometric equations: computational methods
John Voight: On the hypergeometric decomposition of symmetric K3 quartic pencils
Alexander Varchenko: Solutions of KZ differential equations modulo p
Ishai Dan Cohen:The polylog quotient and the Goncharov quotient in computational Chabauty-Kim theory
Henri Cohen: Computing Peterson products in half integral weight after Nelson and Collins
Wadim Zudilin: Many more odd zeta values are irrational
Masha Vlasenko: Dwork Crystals and related congruences
Dali Shen: Interpreting Lauricella hypergeometric system as a Dunkl system
Damian Rössler: The arithmetic Riemann Roch Theorem and Bernoulli numbers