Jan 23, 2023
Monday

09:15 AM  09:30 AM


Welcome

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video


 Abstract
 
 Supplements



09:30 AM  10:30 AM


Euler Systems, LValues, and All That: a Brief Introduction Pt I
Christopher Skinner (Princeton University)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video

 Abstract
This talk is intended as an introduction to the introductory workshop. It will introduce some of the main players  special cohomology classes, Euler systems, padic Lfunctions  largely by focusing on the special case of cyclotomic units and Dirichlet characters.
 Supplements



10:30 AM  11:00 AM


Break

 Location
 
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


Special Cycles on Shimura Varieties and Moduli of Shtukas Pt I
Tony Feng (University of California, Berkeley)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video


 Abstract
I will give an introduction to the theory of special algebraic cycles, emphasizing their relation to arithmetic theta functions. The parallels between the number field (Shimura variety) and function field (moduli of shtukas) situations will be highlighted, and if time permits I will mention some new perspectives from derived algebraic geometry.
 Supplements



12:00 PM  02:00 PM


Lunch

 Location
 
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


Cycles, Motives and Langlands Pt I
Kartik Prasanna (University of Michigan)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video

 Abstract
The Langlands program intersects the theory of motives and algebraic cycles in many different ways. I will talk about some of these, giving a broad overview of the subject, including some recent developments and open problems.
 Supplements


03:00 PM  03:30 PM


Afternoon Tea

 Location
 
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


The Kolyvagin System of Heegner Points Pt I
Giada Grossi (Université de Paris XIII (ParisNord))

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video


 Abstract
Heegner points were introduced in the ‘70s by Birch, inspired by earlier work of Heegner. They are points on rational elliptic curves defined over ring class fields of imaginary quadratic fields and they are a key ingredient to prove much of what is nowadays known about the Birch and SwinnertonDyer conjecture. In these lectures, we will recall their construction and the main results involving them. In particular, we will focus on Kolyvagin’s work, which provides a bound on Selmer groups of elliptic curves. If time permits we will discuss Iwasawa theoretic analogues of this statement (leading to one divisibility in PerrinRiou’s main conjecture) and possible generalisations of the theory of Heegner points.
 Supplements




Jan 24, 2023
Tuesday

08:00 AM  09:00 AM


Iwasawa Theory for Critical Modular Forms
Denis Benois (Université de Bordeaux I)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video


 Abstract
The Iwasawa theory of noncritical modular forms has been extensively studied. I will report on a joint work with Kazim Büyükboduk on Iwasawa theory in the $\theta$critical case. We will give an "étale" construction of Bellaïche's $p$adic $L$functions and discuss the Iwasawa Main Conjecture in this context.
 Supplements



09:30 AM  10:30 AM


Universal Norms and (Phi,Gamma)Modules
Laurent Berger (École Normale Supérieure de Lyon)

 Location
 SLMath: Online/Virtual
 Video

 Abstract
Let K_n=Q_p(mu_{p^n}) for n>0, and let K_infty be the cyclotomic extension of Q_p, namely the union of the K_n. Let Gamma=Gal(K_infty/Q_p). If E is an elliptic curve, or a formal group, the module of universal norms is the projective limit for the trace maps of the E(K_n). What can we say about these universal norms, as a module over the Iwasawa algebra of Gamma? This question has been studied by Mazur, Hazewinkel, Schneider, and others. I will describe a far reaching generalization of this question, that was answered by PerrinRiou using her big exponential map. One can reinterpret PerrinRiou's proof in terms of (phi,Gamma)modules for the cyclotomic extension of Q_p.
 Supplements



10:30 AM  11:00 AM


Break

 Location
 
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


Cycles, Motives and Langlands Pt II
Kartik Prasanna (University of Michigan)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video

 Abstract
 
 Supplements



12:00 PM  02:00 PM


Lunch

 Location
 
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


The Kolyvagin System of Heegner Points Pt II
Giada Grossi (Université de Paris XIII (ParisNord))

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video


 Abstract
Heegner points were introduced in the ‘70s by Birch, inspired by earlier work of Heegner. They are points on rational elliptic curves defined over ring class fields of imaginary quadratic fields and they are a key ingredient to prove much of what is nowadays known about the Birch and SwinnertonDyer conjecture. In these lectures, we will recall their construction and the main results involving them. In particular, we will focus on Kolyvagin’s work, which provides a bound on Selmer groups of elliptic curves. If time permits we will discuss Iwasawa theoretic analogues of this statement (leading to one divisibility in PerrinRiou’s main conjecture) and possible generalisations of the theory of Heegner points.
 Supplements



03:00 PM  03:30 PM


Afternoon Tea

 Location
 
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Special Cycles on Shimura Varieties and Moduli of Shtukas Pt II
Tony Feng (University of California, Berkeley)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video


 Abstract
I will give an introduction to the theory of special algebraic cycles, emphasizing their relation to arithmetic theta functions. The parallels between the number field (Shimura variety) and function field (moduli of shtukas) situations will be highlighted, and if time permits I will mention some new perspectives from derived algebraic geometry.
 Supplements



04:30 PM  06:20 PM


Reception

 Location
 SLMath: Front Courtyard
 Video


 Abstract
 
 Supplements




Jan 25, 2023
Wednesday

09:30 AM  10:30 AM


The PerrinRiou Map and its Use in Iwasawa Theory Pt I
Antonio Lei (University of Ottawa)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video

 Abstract
PerrinRiou's big logarithm map plays an important role in Iwasawa theory. It sends systems of local Galois cohomology clases to padic analytic functions. In particular, it allows us to convert an Euler systems to a padic Lfunction, which is often the first step towards studying Iwasawa main conjectures. I will first review the original construction of this map developed by PerrinRiou and its generalizations. I will then discuss how this map is used in studying Iwasawa theory in several concrete settings.
 Supplements



10:30 AM  11:00 AM


Break

 Location
 
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


Euler Systems, LValues, and All That: a Brief Introduction Pt II
Christopher Skinner (Princeton University)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video

 Abstract
This talk is intended as an introduction to the introductory workshop. It will introduce some of the main players  special cohomology classes, Euler systems, padic Lfunctions  largely by focusing on the special case of cyclotomic units and Dirichlet characters.
 Supplements



12:00 PM  02:00 PM


Lunch

 Location
 
 Video


 Abstract
 
 Supplements



03:00 PM  03:30 PM


Afternoon Tea

 Location
 
 Video


 Abstract
 
 Supplements




Jan 26, 2023
Thursday

09:30 AM  10:30 AM


PAdic LFunctions Pt I
Zheng Liu (University of California, Santa Barbara)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video

 Abstract
I will give an introduction to padic Lfunctions. I will explain the conjecture by Coates and PerrinRiou on the existence of padic Lfunctions and their definition of the modified Euler factors at p for padic interpolations. I will also talk about some approaches for constructing padic Lfunctions with some examples.
 Supplements



10:30 AM  11:00 AM


Break

 Location
 
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


An Introduction to Euler Systems Pt I
Sarah Zerbes (ETH Zürich)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video

 Abstract
Euler systems are one of the most powerful tools for proving new cases of the BirchSwinnertonDyer and BlochKato conjectures. In my lectures, I will give an introduction to the theory of Euler systems, and give some examples of how to construct and where to find them.
 Supplements



12:00 PM  02:00 PM


Lunch

 Location
 
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


Cohomology of Shimura Varieties Pt I
Sug Woo Shin (University of California, Berkeley)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video


 Abstract
 
 Supplements



03:00 PM  03:30 PM


Afternoon Tea

 Location
 
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


The PerrinRiou Map and its Use in Iwasawa Theory Pt II
Antonio Lei (University of Ottawa)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video

 Abstract
PerrinRiou's big logarithm map plays an important role in Iwasawa theory. It sends systems of local Galois cohomology clases to padic analytic functions. In particular, it allows us to convert an Euler systems to a padic Lfunction, which is often the first step towards studying Iwasawa main conjectures. I will first review the original construction of this map developed by PerrinRiou and its generalizations. I will then discuss how this map is used in studying Iwasawa theory in several concrete settings.
 Supplements




Jan 27, 2023
Friday

09:30 AM  10:30 AM


PAdic LFunctions Pt II
Zheng Liu (University of California, Santa Barbara)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video

 Abstract
I will give an introduction to padic Lfunctions. I will explain the conjecture by Coates and PerrinRiou on the existence of padic Lfunctions and their definition of the modified Euler factors at p for padic interpolations. I will also talk about some approaches for constructing padic Lfunctions with some examples.
 Supplements



10:30 AM  11:00 AM


Break

 Location
 
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


An Introduction to Euler Systems Pt II
Sarah Zerbes (ETH Zürich)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video

 Abstract
Euler systems are one of the most powerful tools for proving new cases of the BirchSwinnertonDyer and BlochKato conjectures. In my lectures, I will give an introduction to the theory of Euler systems, and give some examples of how to construct and where to find them.
 Supplements



12:00 PM  02:00 PM


Lunch

 Location
 
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


Cohomology of Shimura Varieties Pt II
Sug Woo Shin (University of California, Berkeley)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video


 Abstract
 
 Supplements



03:00 PM  03:30 PM


Afternoon Tea

 Location
 
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Rigid Meromorphic Cocycles and PAdic Families of Modular Forms
Alice Pozzi (Imperial College, London)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video

 Abstract
Rigid meromorphic cocycles are classes in the first cohomology of SL_2(Z[1/p]) acting on the nonzero rigid meromorphic functions on the Drinfeld padic upper half plane. Their values at real quadratic points are conjectured to be analogues of singular moduli for real quadratic fields. In this talk, I will discuss the relation between real quadratic singular moduli and derivatives of padic families of modular forms. These results can be fit into an emerging padic Kudla program.
 Supplements



