2018.7.6-7.12 学术活动预告
2018/7/5 13:59:31 中国科学院数学与系统科学研究院

     Speaker:

     Zhongzhu Lin, Nanometrics, USA

     Title:

     Representation theoretic and geometric approach to constructing quantum groups.

     Time & Venue:

     2018.7.6 15:00-16:00 N902

     Abstract:

     Since Gabriel's discovery of the one-to-one correspondence between indecomposable representations of a Dynkin quiver and the positive roots of the simple Lie algebra corresponding to the Dynkin diagram, quiver representation theory has been closely tied to Lie algebras in many ways. Ringel's reconstruction of quantum enveloping algebras in terms of Hall algebras of the representations of the Dynkin quiver over finite has lifted connection to a new level and inspired Lusztig to construct the canonical basis. In this talk, I will outline both approaches to constructing quantum groups as well as other subsequent approaches such as Bridgeland's approach in terms of two steps complexes and two parameter quantum groups arising from geometric approach by Fan and Li.

     Speaker:

     Prof. Yunping Jiang，The City University of New York and NSF，USA

     Title:

     Expendability of Holomorphic Motions

     Time & Venue:

     2018.7.6 16:00-17:00 N913

     Abstract:

     In this talk, I will give a review of our work in the study of holomorphic motions of subsets in the Riemann sphere over hyperbolic Riemann surfaces. I will discuss several conditions in the extension problem like the zero-winding number condition, the trivial trace-monodromy condition, the trivial monodromy condition, and the guiding isotopy condition. I will show that all these conditions are necessary in the study of the extension problem. I will use several counter-examples to show that the zero-winding number condition and the trivial trace-monodromy condition are not sufficient. Finally, I will prove that the trivial monodromy condition and the guiding isotopy condition are, indeed, sufficient. In this talk, I will also explain how the study of the lifting problem, which used to be called as one of the most important problems in Teichmueller theory by Bers and Royden, plays an important role in the study of the extension problem in holomorphic motions.

     Speaker:

     Prof.Paulo Ruffino,University of Campinas, Brazil

     Title:

     Bifurcations of stochastic n-point motions

     Time & Venue:

     2018.7.9 10:00 N613

     Abstract:

     We explore the simple observation that a Markov chain with values in a finite space M={1, ..., m }, m=2, has many different extensions to a compatible n-point Markov chain in M^n, for all 1< n < m. Embedding this phenomenon into the context of stochastic (Levy) flows of diffeomorphisms in Euclidean spaces, we introduce the notion of an n-point bifurcation of a stochastic flow. Roughly speaking an n-point bifurcation takes place, when a small perturbation of the stochastic flow does not change the characteristics at lower level k-point motions, k
     Speaker:

     李吉有，上海交通大学数学科学学院

     Title:

     Counting polynomial sums in finite commutative rings

     Time & Venue:

     2018.7.11 15:00 N205

     Abstract:

     Let $R$ be a finite commutative ring and $D$ be a subset of $R$. For a polynomial $f(x)$ in $R[x]$ and a positive integer $k$, we enumerate $k$-subsets $S$ in $D$ such that the polynomial sum over $S$ is a given element. In this talk, I will introduce some recent progress on this problem and its applications in combinatorics, number theory and coding theory.

     This talk is based on joint work with Daqing Wan.

     Speaker:

     Yi Zhang，Institute for Algebra, Johannes Kepler University Linz

     Title:

     Desingularization in the q-Weyl algebra

     Time & Venue:

     2018.7.11 16:00 N205

     Abstract:

     We study the desingularization problem in the first $q$-Weyl algebra. We give an order bound for desingularized operators, and thus derive an algorithm for computing desingularized operators in the first q-Weyl algebra. Moreover, an algorithm is presented for computing a generating set of the first q-Weyl closure of a given q-difference operator. As an application, we certify that several instances of the colored Jones polynomial are Laurent polynomial sequences by computing the corresponding desingularized operator. This is a joint work with Christoph Koutschan.

     Speaker:

     Prof. Yunping Jiang，The City University of New York and NSF，USA

     Title:

     Order of Oscillating Sequences, MMA-MMLS, and Sarnak's Conjecture

     Time & Venue:

     2018.7.17 16:00-17:00 N913

     Abstract:

     In this talk, I will explain several concepts, a log-uniformly oscillation sequence, an oscillation sequence, an oscillation sequence of higher order, a minimal mean attractable (MMA) dynamical system, a minimal mean-L-stable (MMLS) dynamical system. Equicontinuous dynamical systems are clearly MLS. Feigenbaum dynamical systems are not equicontinuous globally but when they are restricted on minimal sets still equicontinuous. Furthermore, in this talk I will give two non-trivial examples of dynamical systems which are not equicontinuous even when they are restricted on minimal sets but MMLS. We will prove that any oscillating sequence is linearly disjoint with all MMA and MMLS dynamical systems. One of the consequences is that Sarnak’s conjecture holds for all MMA and MMLS dynamical systems. There are dynamical systems which are not MMLS. Therefore, we need to use the concept of an oscillation sequence of higher order. The Mobius sequence is an example of an oscillation sequence of higher order due to a result of Hua. In this talk, I will give another interesting example of an oscillation sequence of higher order. Furthermore, I will prove that any oscillation sequence of order $d\geq 2$ is linearly disjoint with all affine distal maps of the $d$-torus.

     来源：中国科学院数学与系统科学研究院

     中国科学院数学与系统科学研究院

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