Explore advanced topics in motivic, equivariant, and non-commutative homotopy theory through this comprehensive summer school featuring mini-courses and research talks by leading mathematicians. Delve into the latest developments in categories of motives, calculational and foundational aspects of motivic and equivariant homotopy theory, and generalizations of these tools in non-commutative geometry settings. Learn from distinguished speakers including Clark Barwick, Teena Gerhardt, Daniel Isaksen, Dmitry Kaledin, Marc Levine, Ivan Panin, and Gonçalo Tabuada through structured mini-course series covering enumerative geometry and quadratic forms, algebraic K-theory and trace methods, motives from the non-commutative perspective, motivic and equivariant stable homotopy groups, exodromy for ℓ-adic sheaves, and noncommutative counterparts of celebrated conjectures. Engage with cutting-edge research presentations on topics including motivic realizations of singularity categories, local construction of stable motivic homotopy theory, pullbacks for the Rost-Schmid complex, fibrant resolutions of motivic Thom spectra, equivariant infinite loop space machines, knots and motives, triangulated categories of log motives, real and hyperreal equivariant computations, and integrability results for A¹-Euler numbers. Gain insights into three rapidly developing mathematical fields where long-standing conjectures have been recently solved, existing theories are being refined, and new foundational developments are emerging that promise to drive future advances and interdisciplinary interactions.

Syllabus

Marc Levine - 1/3 Enumerative Geometry and Quadratic Forms
Teena Gerhardt - 1/3 Algebraic K-theory and Trace Methods
Dmitry Kaledin - 1/3 Motives from the Non-commutative Point of View
Daniel Isaksen - 1/3 Motivic and Equivariant Stable Homotopy Groups
Teena Gerhardt - 2/3 Algebraic K-theory and Trace Methods
Clark Barwick - 1/3 Exodromy for ℓ-adic Sheaves
Clark Barwick - 2/3 Exodromy for ℓ-adic Sheaves
Marc Levine - 2/3 Enumerative Geometry and Quadratic Forms
Dmitry Kaledin - 2/3 Motives from the Non-commutative Point of View
Teena Gerhardt - 3/3 Algebraic K-theory and Trace Methods
Daniel Isaksen - 2/3 Motivic and Equivariant Stable Homotopy Groups
Marc Levine _ 3/3 Enumerative Geometry and Quadratic Forms
Dianel Isaksen - 3/3 Motivic and Equivariant Stable Homotopy Groups
Clark Barwick - 3/3 Exodromy for ℓ-adic Sheaves
Dmitry Kaledin - 3/3 Motives from the Non-commutative Point of View
Gonçalo Tabuada - 1/3 Noncommutative Counterparts of Celebrated Conjectures
Marco Robalo - Motivic Realizations of Singularity Categories
Ivan Panin - 1/3 A Local Construction of Stable Motivic Homotopy Theory
Tom Bachmann - Pullbacks for the Rost-Schmid Complex
Alexander Neshitov - Fibrant Resolutions of Motivic Thom Spectra
Ivan Panin 2/3 - A Local Construction of Stable Motivic Homotopy Theory
Angélica M. Osorno - Equivariant Infinite Loop Space Machines
Geoffroy Horel - Knots and Motives
Gonçalo Tabuada - 3/3 Noncommutative Counterparts of Celebrated Conjectures
Ivan Panin 3/3 - A Local Construction of Stable Motivic Homotopy Theory
Federico Binda - Triangulated Categories of Log Motives over a Field
Mike Hill - Real and Hyperreal Equivariant and Motivic Computations
Kirsten Wickelgren - Integrability Result for ^1-Euler Numbers