#### ** Upcoming Talk**

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**May 31 (Wed.)**** 11:00-12:30**

Dr. Hsiao-Fan Liu (Academia Sinica)

Venue: Room 202, Astro-Math. Building

Title: An introductory on discrete versions of Painlevé equations

**Abstract:**

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The six Painlevé equations $(P_I − P_{VI})$ play an important role in many areas of mathematics and physics, and the connection with integrable systems has been well-established. Recently, discrete integrable systems have gained more attention and hence it is natural to consider discrete versions of Painlevé equations. In this talk, we will present discrete forms of the $P_{III}$, $P_{IV}$ and $P_V$. These mappings go over to the Painlevé equations in the continuous limit. The singularity confinement test as a discrete analogue of the Painlevé property will be also discussed. **

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**June 7 (Wed.)**** 11:00-12:30**

Dr. Taiji Marugame (Academia Sinica)

Venue: Room 202, Astro-Math. Building

Title: Construction of global CR invariants via Cheng-Yau metric

**Abstract:**

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Strictly pseudoconvex domains in a Stein manifold admit a complete Kahler-Einstein metric called the Cheng-Yau metric. In this talk, I present two methods of constructing global CR invariants of the boundary using this metric. The first is the renormalized Chern-Gauss-Bonnet formula, which gives a higher dimensional generalization of the Burns-Epstein invariant. The second is the renormalized volume, which is shown to agree with the integral of the CR Q-prime curvature of the boundary. The second construction is joint work with K. Hirachi and Y. Matsumoto. **

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**June 14 (Wed.)**** 11:00-12:30**

Dr. Chih-Whi Chen (National Center for Theoretical Sciences)

Venue: Room 201, Astro-Math. Building

Title: Affine periplectic Brauer algbera

**Abstract:**

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The periplectic Lie superalgebra p(n) is a superanalogue of the orthogonal or symplectic Lie algebra preserving an odd non-degenerate symmetric or skew-symmetric bilinear form. Moon used generator and relation to define the periplectic Brauer algebra, which can be used to describe the endomorphism algebra of tensor power of natural representations of p(n). Recently, Kujawa and Tharp gave diagrammatic description of this algebra.
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In this talk, we will first recall Moon's Schur-Weyl duality for p(n). We will formulate a degenerate affine version of periplectic Brauer algebra including its diagram interpretation. This is a joint work with Yung-Ning Peng.
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