Talk 1: Introduction to Quantum K-theory. Speaker: Y.P. Lee ( University of Utah) Abstract: The basics of quantum K-theory will be explained, assuming only rudiments of quantum cohomology. This will be followed by an advanced talk on quantum K-theory, given by Dr. Tonita in this colloquium. Talk 2: K-theoretic GW invariants. Speaker: Valentin Tonita (Institute de Mathematiques Jussieu) Abstract: K-theoretic Gromov-Witten invariants have been introduced by A. Givental and Y.- P. Lee: they are holomorphic Euler characteristics of certain vector bundles on the moduli spaces of stable maps to a (complex) projective manifold X. In this talk I will define the invariants, describe some relations among them and explain how - in genus zero - they are related to the cohomological Gromov Witten invariants of X (the last part is joint work with A. Givental). Talk3: A reconstruction theorem in quantum K-theory. Speaker: Valentin Tonita (Institute de Mathematiques Jussieu) Abstract: One can use the genus 0 K-theoretic GW invariants of X to define the quantum K- theoretic product - a deformation of the tensor product in K*(X). I will show how to reconstruct this product from the small J-function of X - under some line bundle generation condition on K*(X) - using the D-module structure in quantum K-theory (which in its turn is a consequence of the main theorem in the previous talk). This is joint work with H. Iritani and T. Milanov. Talk 4: Gromov--Witten theory and variation of Hodge structure under conifold transitions for Calabi-Yau threefolds. Speaker: Y.P. Lee ( University of Utah) Abstract: The moduli of Calabi--Yau threefolds are generally believed to be connected by a geometric process called transition, which is roughly speaking degeneration followed by small resolution. In this talk, I will explain a phenomenon of partial exchange of A model (Gromov--Witten theory) and B model (variation of Hodge structure) when a Calabi--Yau threefold undergoes a conifold transition. This suggests a possibility of an "A+B theory" which is invariant under transitions. This talk is based on joint work with H.-W. Lin and C.-L. Wang. Talk 5. Title: Two approaches towards Landau-Ginzburg mirror symmetry Speaker: Yefeng Shen (Kavli IPMU，Tokyo) Abstract: In this talk, I will describe two approaches towards Landau-Ginzburg mirror symmetry between FJRW theory and Saito-Givental theory for a Fermat singularity. The first approach relies on the reconstruction using WDVV equations and a perturbative formula developed by Li-Li-Saito in the theory of primitive forms. The second approach relies on toric geometry and I-functions in Fan-Jarvis-Ruan's construction of Gauged Linear Sigma Models. My talk is based on works of He-Li-Shen-Webb and Iritani-Milanov-Ruan-Shen.