Department of

Mathematics


Seminar Calendar
for Graduate Student Number Theory Seminar events the year of Friday, September 14, 2018.

     .
events for the
events containing  

(Requires a password.)
More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2018           September 2018          October 2018    
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
           1  2  3  4                      1       1  2  3  4  5  6
  5  6  7  8  9 10 11    2  3  4  5  6  7  8    7  8  9 10 11 12 13
 12 13 14 15 16 17 18    9 10 11 12 13 14 15   14 15 16 17 18 19 20
 19 20 21 22 23 24 25   16 17 18 19 20 21 22   21 22 23 24 25 26 27
 26 27 28 29 30 31      23 24 25 26 27 28 29   28 29 30 31         
                        30                                         

Thursday, February 1, 2018

2:10 pm in 241 Altgeld Hall,Thursday, February 1, 2018

Modular Forms and Moduli of Elliptic Curves

Ningchuan Zhang (UIUC)

Abstract: In this talk, Iíll explain why modular forms are global sections of the sheaf of invariant differentials over the moduli stack of elliptic curves. In the end, Iíll mention the $q$-expansion principle and integral modular forms. No knowledge of stack is assumed for this talk. Please note this talk will start 10 minutes later than the regular time.

Thursday, February 8, 2018

2:00 pm in 241 Altgeld Hall,Thursday, February 8, 2018

Multiplicative functions which are additive on polygonal numbers

Byungchan Kim (SeoulTech)

Abstract: Spiro showed that a multiplicative function which is additive on prime numbers should be the identity function. After Spiro's work, there are many variations. One direction is to investigate multiplicative functions which are additive on polygonal numbers. It is known that a multiplicative function which is additive on triangular numbers should be the identity while there are non-identity functions which is multiplicative and is additive on square numbers. In this talk, we investigate multiplicative functions which are additive on several polygonal numbers and present some open questions. This talk is based on joint works with J.-Y. Kim, C.G. Lee and P.-S. Park.

Thursday, February 15, 2018

2:00 pm in 241 Altgeld Hall,Thursday, February 15, 2018

p-adic families of modular forms

Ravi Donepudi   [email] (UIUC)

Abstract: This talk is an introduction to the theme of p-adic variation in number theory, especially concerning modular forms. We will first give a general overview of the p-adic Galois representation attached to a classical Hecke eigenform. Then we will closely study the example of Eisenstein series which are classically parametrized by integer weights and see how they can be naturally interpolated p-adically to give a family of p-adic modular forms. As a corollary, this yields a very simple construction of p-adic L-functions. Finally we will tie these two themes together to study the structure of p-adic Galois representations arising from modular forms in the larger space of all p-adic Galois representations (of a fixed Galois group), highlighting GouvÍa-Mazurís construction of the ďinfinite fern of Galois representations" and Coleman-Mazurís Eigencurve. Have I mentioned the word ďp-adicĒ yet?

Thursday, February 22, 2018

2:00 pm in 241 Altgeld Hall,Thursday, February 22, 2018

Multiples of long period small element continued fractions to short period large elements continued fractions

Michael Oyengo (UIUC)

Abstract: We construct a class of rationals and quadratic irrationals having continued fractions whose period has length $n\geq2$, and with "small'' partial quotients for which certain integer multiples have continued fractions of period $1$, $2$ or $4$ with "large'' partial quotients. We then show that numbers in the period of the new continued fraction are simple functions of the numbers in the periods of the original continued fraction. We give generalizations of these continued fractions and study properties of polynomials arising from these generalizations.

Thursday, March 1, 2018

2:00 pm in 241 Altgeld Hall,Thursday, March 1, 2018

Spectral Theory on the Modular Surface

Hadrian Quan   [email] (UIUC)

Abstract: Many questions about number fields can be recast as questions regarding Laplace eigenvalues on certain manifolds. In this talk Iíll discuss some ideas and results related to Selbergís trace formula, how partial results towards Selbergís $\frac{1}{4}$-conjecture have immediate applications, and why number theorists might care about the analysis of Laplacians to begin with.

Thursday, March 8, 2018

2:00 pm in Altgeld Hall,Thursday, March 8, 2018

Cancelled

Thursday, March 15, 2018

2:00 pm in 241 Altgeld Hall,Thursday, March 15, 2018

Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels

Hsin-Po Wang (UIUC)

Abstract: We will talk about https://arxiv.org/abs/0807.3917 Polar code is considered one of the best codes in the world (together with LDPC and Turbo code). Following Arikan's paper, we will define polar code from scratch and prove that it achieve capacity. If time permits, we will talk about implementation details; in particular comparing virtual channels in an engineering-friendly way. If time still permits, we will talk about how fast does it achieve capacity.

Thursday, March 29, 2018

2:00 pm in 241 Altgeld Hall,Thursday, March 29, 2018

Restriction estimates and their applications in number theory

Fernando Xuancheng Shao   [email] (University of Kentucky)

Abstract: I will survey recent developments on restriction theory for exponential sums over sets of number theoretic interest, such as primes, smooth numbers, and k-th powers, and their applications to analytic number theory and additive combinatorics, including Roth-type theorems in primes and Waring-type results in smooth k-th powers.

Thursday, April 12, 2018

2:00 pm in 241 Altgeld Hall,Thursday, April 12, 2018

Spectral Theory on the Modular Surface

Hadrian Quan   [email] (UIUC)

Abstract: Many questions about number fields can be recast as questions regarding Laplace eigenvalues on certain manifolds. In this talk Iíll discuss some ideas and results related to Selbergís trace formula, how partial results towards Selbergís $\frac{1}{4}$-conjecture have immediate applications, and why number theorists might care about the analysis of Laplacians to begin with.

Thursday, April 26, 2018

2:00 pm in 241 Altgeld Hall,Thursday, April 26, 2018

The p-torsion of Ree curves

Dane Skabelund (UIUC)

Abstract: This talk will describe some recent computations involving the structure of 3-torsion of the Ree curves, which are a family of supersingular curves in characteristic 3.

Thursday, August 30, 2018

2:00 pm in 241 Altgeld Hall,Thursday, August 30, 2018

Organizational Meeting

Kyle Pratt (UIUC)

Abstract: We will have a short meeting to draw up a schedule of speakers for the semester. Please sign up if you have a topic in mind! All are welcome, and cookies will be provided.

Thursday, September 13, 2018

2:00 pm in 241 Altgeld,Thursday, September 13, 2018

The Combinatorics of Second Order Mock Theta Functions

Hannah Burson (University of Illinois at Urbana-Champaign)

Abstract: Less than a year before his death, Ramanujan wrote a letter to Hardy introducing mock theta functions and listing 17 examples of such functions. Zwegers' 2002 thesis allowed for the discovery of infinite families of mock theta functions. The second order mock theta functions are an example of more recently discovered mock theta functions. This talk will introduce new combinatorial interpretations of a general second-order mock theta function identity. In the process, we will talk about some famous results in the theory of partitions and some of the history of Ramanujan.