#### ** Upcoming Talk**

**November 27, 2019 (Wed.)**** 11:00-12:30**

Sanghyuck Moon (National Center for Theoretical Sciences)

Venue: Room 638, Astro-Math. Building

Title: Variational methods for an elliptic equation and system

**Abstract:**

**We will see two elliptic problems and construct solutions by variational methods. The first problem is a singularly perturbed Neumann problem with a general nonlinearity term and spike layer solutions for the problem. The second problem is the asymptotic behavior of solutions for coupled Schroedinger equations with mixed interactions. The components of solutions exhibit partial synchronization and segregation when attractive and repulsive couplings are simultaneously large. I will explain the development of results and ideas of variational approach for these problems.
**

**
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**December 4, 2019 (Wed.)**** 11:00-12:30**

Arasteh Rad (National Center for Theoretical Sciences)

Venue: Room 638, Astro-Math. Building

Title: Langlands Program and Manifestations of Shtukas

**December 4, 2019 (Wed.)**

**11:00-12:30**

Arasteh Rad (National Center for Theoretical Sciences)

Venue: Room 638, Astro-Math. Building

Title: Langlands Program and Manifestations of Shtukas

**
**

**Abstract:**

**Moduli spaces for (G-)shtukas appear as function fields analogs for Shimura varieties. This can be observed through so-called Langlands philosophy. In this talk we aim to review the big underlying picture. In addition we will discuss the construction of these spaces. We do this from a new point of view. As we will see, this may shed some light on the possible relations between these moduli spaces and some other interesting (and well-known) moduli spaces. We further briefly mention some methods to describe the local geometry of these spaces.
**