Speaker: Bo-Hae Im (Chung-Ang University)
Title: The growth of the rank of abelian varieties over certain Galois extensions
Abstract: We consider various Galois extensions over which certain abelian varieties has rank growth. In particular, in geometric approach we give a condition when there is a rational curve in the quotient of an abelian variety by some finite groups, and apply this to construct the rank growth. Also we show  that if $mathcal{X}$ is a Riemann surface of genus $g>1$ defined over a number field $K$ which is a degree $d$-covering of $mathbb{P}^1_K$, then there are infinitely many linearly disjoint degree $d$-extensions $L/K$ over which the Jacobian of $mathcal{X}$ gains rank.  For the genus $1$ case, we show the existence of infinitely many elliptic curves that gain rank over infinitely many cyclic cubic extensions of $mathbb{Q}$. This is a joint work with Erik Wallace.

Speaker: Masanobu Kaneko (Kyushu Univ.)
Title: A new integral-series identity of multiple zeta values and regularizations
Abstract: We present a new ``integral = series'' type identity of multiple zeta values, and show that this is equivalent in a suitable sense to the fundamental theorem of regularization. We conjecture that this identity is enough to describe all linear relations over the rationals of multiple zeta values. This is a joint work with Shuji Yamamoto.

Speaker: Subong Lim (Sungkyunkwan Univ.)
Title: Limits of traces of singular moduli
Abstract: Zagier proved that traces $Tr_d(j_1)$ of singular moduli for $d<0$ are coefficients of a weakly holomorphic modular form $g_1$ of weight $3/2$. Duke, Imamo$bar{mathrm{g}}$lu, and T'oth defined a modular trace $Tr_d(j_1)$ for $d>0$ by using the cycle integral of $j_1$, and showed that its generating function is a mock modular form whose shadow is $g_1$. In this talk, we introduce connections between $Tr_d(j_1)$ for $d>0$ and $Tr_d(j_1)$ for $d<0$ by considering a certain asymptotic behavior of twisted sums of $Tr_d(j_1)$ over $d>0$ and $d<0$, respectively.

Speaker: Yoichi Mieda (Univ. of Tokyo)
Title: Cohomology of affinoids in the Lubin-Tate space at infinite level and their reductions
Abstract: Under some conditions, I will compare the l-adic cohomology of an affinoid in the Lubin-Tate space at infinite level and that of the reduction of its formal model. I will also give some applications.

Speaker: Chol Park (KIAS)
Title: Mod~$p$ local-global compatibility for $GL_3(Q_p)$ in the non-ordinary case
Abstract: Let $F/Q$ be a CM field in which $p$ splits completely and $r$ a 3-dimensional continuous modular Galois representation of $G_F$ over an algebraic closed field of the finite filed of order~$p$. We assume that $r|_{G_{F_w}}$ is a non-trivial extension of two dimensional irreducible representation by a character at a place~$w$ above~$p$. In this talk, we discuss a problem about local-global compatibility in the mod~$p$ Langlands program for $GL_3(Q_p)$. We define a local invariant associated to $r|_{G_{F_w}}$ in terms of Fontaine-Laffaille theory and provide a nearly optimal weight elimination result as well as the modularity of the obvious weights of $r$. It is expected that if $r|_{G_{F_w}}$ is split, then it is determined by the set of modular Serre weights and the Hecke action on its constituents. However, this is not true if $r|_{G_{F_w}}$ is non-split, and the question of determining $r|_{G_{F_w}}$ from a space of mod $p$ automorphic forms lies deeper than the weight part of Serre's conjecture. We show that the local invariant associated to $r|_{G_{F_w}}$ can be obtained in terms of a refined Hecke action on a space of mod~$p$ algebraic automorphic forms on a compact unitary group. This is a joint work with Daniel Le and Stefano Morra.

Speaker: Takeshi Saito (Univ. of Tokyo)
Title: On the characteristic cycle of a constructible sheaf
Abstract: For a constructible sheaf on a smooth scheme over a perfect field, the characteristic cycle is defined as a cycle on the cotangent bundle supported on the singular support. After briefly recalling the definition, I will discuss some of properties, including functoriality.

Speaker: Atsushi Shiho (Univ. of Tokyo)
Title: Isocrystals on simply connected varieties
Abstract: It is conjectured by de Jong that, on a simply connected projective smooth variety over an algebraically closed field of positive characteristic, any isocrystal is constant (a finite direct sum of structure isocrystals).
In this talk, we give a proof of this conjecture under certain additional assumptions. This is a joint work with Hélène Esnault.

Speaker: Sug Woo Shin( UC Berkeley/KIAS)
Title: Galois representations for general symplectic groups
Abstract: We prove the existence of GSpin-valued Galois representations corresponding to regular algebraic cuspidal automoprhic representations of general symplectic groups under simplifying local hypotheses. This is joint work with Arno Kret.

Speaker: Hae-Sang Sun (UNIST)
Title: Modular symbols and special L-values modulo prime
Abstract: In the talk, we introduce a submodule of the first homology group of a modular curve generated by special modular symbols. We also present a conjecture on the submodule, which implies two conjectures, namely a modular analogue of Washington's theorem and Greenberg conjecture on the mu invariant of Mazur-Swinnerton-Dyer p-adic L-function. One evidence of the conjecture, namely full-rankness of the submodule and its consequences, namely some partial results on the previous two conjectures will be discussed. This is a joint work with Myoungil Kim (UNIST).

Speaker: Takashi Taniguchi (Kobe Univ.)
Title: Orbital exponential sums associated to prehomogeneous vector spaces
Abstract: For a prehomogeneous vector space (G,V) defined over a finite field, it is natural to associate a multidimensional exponential sum, or equivalently, a Gauss sum with the trivial character. It is a Fourier transform associated to the characteristic function of any of the G-orbits over the finite field. In this talk we develop a simple new method to evaluate these sums, and apply it in several of case. After that we discuss its applications to number theory. This is a joint work with Frank Thorne.