Organizers
The UCSD number theory group with support from NSF and UCSD.
Invited speakers
Serin Hong (University of Arizona), Kevin McGown (CSU Chico), Andrea Pulita (Université Grenoble Alpes/UCSD), Allechar Serrano López (Montana State University)
Location
The conference will be hybrid. The talks will be held in person in
AP&M
Bldg. (Dept. of Math.) Room 6402, on the UCSD campus and also available remotely via
Zoom.
For directions and more information, click
here.
Zoom
The Zoom meeting code is 993 5967 5186; the password is the fourdigit number of the room where the conference is taking place.
Registation
If you are planning to come in person, please fill out the
registration form by
Wednesday February 21, 2024.
Lunch options
See
here for a list of options on campus. Or just follow the locals.
Dinner
Pizza! We will have pizza from Regents pizzeria (the good stuff!) and in order to make sure we order enough please fill out the
registration form by
Wednesday February 21, 2024.
Health and safety
We strongly encourage everyone to be fully vaccinated against COVID19 (including the latest boosters) and to get tested beforehand. If you feel under the weather, we suggest you take advantage of the Zoom option.
Parking
If you are a UCSD affiliate, surely you've had to solve this problem before. This information is mostly for visitors.
You will have to pay either by using the
ParkMobile app or pay by credit card (Visa, Mastercard, or American Express) at the nearest pay station. Unless you are a UCSD affiliate you will have to park in a
visitor parking spot (marked
V) and use the ParkMobile zone
4752.
The closest parking structures to AP&M are the following, in order of distance.
 Scholars Parking Structure (Sixth College): V spots on level B1 (map)
 Pangea Parking Structure (Roosevelt College): V spots on level 6, 7 (map)
 Osler Parking Structure (South Parking Structure): V spots on level 3 (map)
 Gilman Parking Structure: V spots on levels 13 (map)
Schedule (all times PST)
9:3010:30am  
Andrea Pulita (Université Grenoble Alpes/UCSD) De Rham cohomology of padic differential equations 

10:3011:00am  
Coffee/tea break


11:00am12:00pm  
Allechar Serrano López (Montana State University) Counting number fields 

12:002:30pm  
Lunch break


2:303:30pm  
Kevin McGown (CSU Chico) An improved error term for counting D_{4}quartic fields 

3:304:00pm  
Coffee/tea break


4:005:00pm  
Serin Hong (University of Arizona) A nonemptiness criterion for Newton strata 

5:45pm  
Dinner (pizza will be served) 
Abstracts
Serin Hong (University of Arizona)
A nonemptiness criterion for Newton strata
The notion of Newton stratification originates from Grothendieck's work on the moduli space of abelian varieties. Since its inception, the notion has significantly evolved to find many applications in arithmetic geometry, including the study of Shimura varieties and the local Langlands correspondence. We describe various formulations of the Newton stratification, and discuss the question of determining all nonempty strata.
Kevin McGown (CSU Chico)
An improved error term for counting D_{4}quartic fields
It is an interesting problem to find asymptotic expressions for the number of degree n number fields with specified Galois closure G and bounded discriminant. We prove that the number of quartic fields K with discriminant less than X
whose Galois closure is D_{4} equals CX +O(X^{5/8+ε}), improving the error term
in a wellknown result of Cohen, Diaz y Diaz, and Olivier. In order to carry
this out, we establish a result for counting relative quadratic extensions with
a power saving error term for which the implicit constant only depends on the
degree of the base field. This is joint work with Amanda Tucker.

Andrea Pulita (Université Grenoble Alpes/UC San Diego)
De Rham cohomology of padic differential equations
I'll give an overview on a series of results of the last decade to which I had the opportunity to give a contribution. I'll focus in particular on de Rham cohomology and finite dimensionality criteria.

Allechar Serrano López (Montana State University)
Counting number fields
A guiding question in arithmetic statistics is: Given a degree n and a Galois group G in S_{n}, how does the count of number fields of degree n whose normal closure has Galois group G grow as their discriminants tend to infinity? In this talk, I will give an overview of the history and development of number field asymptotics and we will obtain a count for dihedral quartic extensions over a fixed number field.