Southern California Number Theory Day

The UCSD number theory group with support from NSF and UCSD.

Serin Hong (University of Arizona), Kevin McGown (CSU Chico), Andrea Pulita (Université Grenoble Alpes/UCSD), Allechar Serrano López (Montana State University)

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.

The Zoom meeting code is 993 5967 5186; the password is the four-digit number of the room where the conference is taking place.

If you are planning to come in person, please fill out the registration form by Wednesday February 21, 2024.

See here for a list of options on campus. Or just follow the locals.

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.

We strongly encourage everyone to be fully vaccinated against COVID-19 (including the latest boosters) and to get tested beforehand. If you feel under the weather, we suggest you take advantage of the Zoom option.

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 1-3 (map)

• 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.

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• Kevin McGown (CSU Chico)
  An improved error term for counting D₄-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 D₄ equals CX +O(X^5/8+ε), improving the error term in a well-known 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.

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• Andrea Pulita (Université Grenoble Alpes/UC San Diego)
  De Rham cohomology of p-adic 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.

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• 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.

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