Starting from Fall 2019, we organize the Calgary Algebra & Number Theory Seminar. While talks in Fall 2019 are scheduled in an ad hoc manner, we aim to have a more regular seminar starting from Spring 2020. Here Algebra and Number Theory (ANT) are interpreted broadly. If you work in related aspects of ANT and like to give a talk here, feel free to contact us: Thomas Bitoun (thomas.bitoun@ucalgary.ca) or Dang-Khoa Nguyen (dangkhoa.nguyen@ucalgary.ca).

Fall 2019:

• October 23, 3pm-4pm at MS 337:

Densities of eigenspaces of Frobenius and distributions of R-modules by Jack Klys (UCalgary).

Abstract: We will discuss density theorems for Jacobians of hyperelliptic curves over finite fields (in the large genus limit), viewed as modules over the Frobenius. Our work builds on recent advances in this area by Ellenberg-Venkatesh-Westerland and Lipnowski-Tsimerman. The methods involve the study of measures on R-modules over rings R which are finite Z_p-algebras. As an application, for any polynomial p(x) over F_p we determine an explicit formula for the asymptotic density of hyperelliptic curves for which p(x) divides the characteristic polynomial of Frobenius acting on the p-torsion of the Jacobian. Joint work with Jacob Tsimerman.

• November 1 (2 talks), 11am-12pm at MS 427:

Torsion points modulo primes and their applications by Amir Akbary (ULethbridge)

Abstract: click here.

• November 1 (2 talks), 2pm-3pm at MS 427:

Extension of Ramanujan-Mordell formula with coefficients 1 and $p$ by Zafer Selcuk Aygin (ULethbridge)

Abstract: click here.

Winter 2020:

• Thursday January 30, 1pm-2pm at MS 427:

Explicit results about primes in Chebotarev's density theorem by Habiba Kadiri (ULethbridge)

Abstract: click here.

• Thursday February 20, 1pm-2pm at MS 427:

Entropy of non-Archimedean endomorphisms by Charles Favre (École Polytechnique and UBC)

Abstract: click here.

• Thursday March 5, 1pm-2pm at MS 427:

Moments of the Riemann zeta function and mean values of long Dirichlet polynomials by Nathan Ng (ULethbridge)

Abstract: click here.

The remaining talks have been cancelled due to Covid-19. Special thanks to Avi Kulkarni, Shabnam Akhtari, Uli Walther, Peter Koymans, and Carlo Pagano who had agreed to visit us and had to cancel their trips.