Home /  Introductory Workshop: Algebraic Cycles, L-Values, and Euler Systems

Workshop

Introductory Workshop: Algebraic Cycles, L-Values, and Euler Systems January 23, 2023 - January 27, 2023
Registration Deadline: January 27, 2023 almost 2 years ago
To apply for Funding you must register by: October 23, 2022 about 2 years ago
Parent Program:
Location: SLMath: Eisenbud Auditorium, Atrium
Organizers Henri Darmon (McGill University), LEAD Ellen Eischen (University of Oregon), Benjamin Howard (Boston College), Elena Mantovan (California Institute of Technology)
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Description
Image
Image credit: Vincent J. Matsko, 6-adic Koch-like fractal. For details, see http://www.vincematsko.com/Art/ICERM.html
This will be a hybrid workshop with both in-person and virtual participation. This workshop is held in honor of mathematician Bernadette Perrin-Riou. Bernadette Perrin-Riou, one of the pioneering figures in Iwasawa Theory in the 1990s, is widely acclaimed for the influential ideas she has brought to the subject. Her deep study of the Euler system originally constructed by Kato led to the introduction of her fundamental "big logarithm map" (often referred to as the "Perrin-Riou map" nowadays), which is a far reaching generalisation of the Coleman power series and is one of the key ingredients in establishing links between Euler systems and p-adic L-functions. Her work also initiated the study of higher rank Euler systems and has been a source of inspiration for many further developments in this direction. Likewise, her p-adic analogue of the Gross-Zagier formula has opened up an area of inquiry that remains active and fertile to the present day. All these, as well as many other important contributions of Perrin-Riou, continue to serve as a model and a guide for today's research in Iwasawa Theory. This workshop is therefore dedicated to the celebration of her 68th birthday. The Introductory Workshop aims to provide a coherent overview of current research in algebraic cycles, L-values, Euler systems, and the many connections between them. This includes the study of special cycles on Shimura varieties and moduli spaces of shtukas, integral representations of L-values and the construction of p-adic L-functions, and the construction of Euler systems from special elements in Chow groups or higher Chow groups of Shimura varieties. Workshop lectures will be organized into short lecture series, so as to allow each series to begin with expository lectures on foundational results before moving on to current research. The workshop is being paired with a Tuesday activity in Paris celebrating the mathematical  influence of Perrin-Riou: Journée "Algebraic Cycles, L-values and Euler Systems" à Paris en l'honneur de Bernadette Perrin-Riou For details on the image, see http://www.vincematsko.com/Art/ICERM.html
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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent PhDs, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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For information about recommended hotels for visits of under 30 days, visit Short-Term Housing. Questions? Contact coord@slmath.org.

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Schedule, Notes/Handouts & Videos
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Jan 23, 2023
Monday
09:15 AM - 09:30 AM
  Welcome
09:30 AM - 10:30 AM
  Euler Systems, L-Values, and All That: a Brief Introduction Pt I
Christopher Skinner (Princeton University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Special Cycles on Shimura Varieties and Moduli of Shtukas Pt I
Tony Feng (University of California, Berkeley)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Cycles, Motives and Langlands Pt I
Kartik Prasanna (University of Michigan)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  The Kolyvagin System of Heegner Points Pt I
Giada Grossi (Université de Paris XIII (Paris-Nord))
Jan 24, 2023
Tuesday
08:00 AM - 09:00 AM
  Iwasawa Theory for Critical Modular Forms
Denis Benois (Université de Bordeaux I)
09:30 AM - 10:30 AM
  Universal Norms and (Phi,Gamma)-Modules
Laurent Berger (École Normale Supérieure de Lyon)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Cycles, Motives and Langlands Pt II
Kartik Prasanna (University of Michigan)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  The Kolyvagin System of Heegner Points Pt II
Giada Grossi (Université de Paris XIII (Paris-Nord))
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  Special Cycles on Shimura Varieties and Moduli of Shtukas Pt II
Tony Feng (University of California, Berkeley)
04:30 PM - 06:20 PM
  Reception
Jan 25, 2023
Wednesday
09:30 AM - 10:30 AM
  The Perrin-Riou Map and its Use in Iwasawa Theory Pt I
Antonio Lei (University of Ottawa)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Euler Systems, L-Values, and All That: a Brief Introduction Pt II
Christopher Skinner (Princeton University)
12:00 PM - 02:00 PM
  Lunch
03:00 PM - 03:30 PM
  Afternoon Tea
Jan 26, 2023
Thursday
09:30 AM - 10:30 AM
  P-Adic L-Functions Pt I
Zheng Liu (University of California, Santa Barbara)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  An Introduction to Euler Systems Pt I
Sarah Zerbes (ETH Zürich)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Cohomology of Shimura Varieties Pt I
Sug Woo Shin (University of California, Berkeley)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  The Perrin-Riou Map and its Use in Iwasawa Theory Pt II
Antonio Lei (University of Ottawa)
Jan 27, 2023
Friday
09:30 AM - 10:30 AM
  P-Adic L-Functions Pt II
Zheng Liu (University of California, Santa Barbara)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  An Introduction to Euler Systems Pt II
Sarah Zerbes (ETH Zürich)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Cohomology of Shimura Varieties Pt II
Sug Woo Shin (University of California, Berkeley)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  Rigid Meromorphic Cocycles and P-Adic Families of Modular Forms
Alice Pozzi (Imperial College, London)