"강연은 아래와 같은 순서로 진행됩니다."

Speaker: 김동한 (동국대)
Title: A new complexity function of repetition and irrationality exponents
Abstract: We introduce and study a new complexity function in combinatorics on words, which takes into account the smallest return time of a factor of an infinite word. We characterize the eventually periodic words and the Sturmian words by means of this function. Then, we establish a new result on repetitions in Sturmian words and show that it is best possible. We deduce a lower bound for the irrationality exponent of real numbers whose sequence of b-ary digits is a Sturmian sequence over {0,1,…,b−1} and we prove that this lower bound is best possible. If the irrationality exponent of ￦xi is equal to 2 or slightly greater than 2, then the b-ary expansion of ￦xi cannot be 'too simple', in a suitable sense. Our result applies, among other classical numbers, to badly approximable numbers, non-zero rational powers of e, and log(1+1/a), provided that the integer a is sufficiently large. It establishes an unexpected connection between the irrationality exponent of a real number and its b-ary expansion.
This is joint work with Yann Bugeaud.

Speaker: 이상진 (건국대)
Title: Braid groups and RAAGs
Abstract: In this talk, I will introduce braid groups, unknotting number of 3-braid knots, embedding of right-angled Artin groups into braid groups.

Speaker: 박미희 (중앙대)
Title: Content formulas in polynomial and power series rings
Abstract:


Speaker: 김남권 (조선대)
Title: Mathematical analysis on nontopological vortex and mixed type votex in some gauge theories
Abstract: We present here some recent results on existence of a nontopological and mixed type vortex in several gauge theories. Nontopological vortex is a symmetrically decaying vortex and mixed type vortex is asymmetrically decaying. Existence of such objects is a highly nontrivial question and require subtle analysis. We briefly mention the difficulties and key ideas in this problem.

Speaker: 전대열 (공주대)
Title: Torsion subgroups of elliptic curves over number fields
Abstract: In this talk, we give a brief summary to the recent results on the torsion subgroups of elliptic curves over number fields.

Speaker: 권재훈 (서울대)
Title: Kac-Wakimoto conjecture for simple Lie superalgebras
Abstract: The character of the finite-dimensional simple modules over a finite-dimensional simple Lie algebra is given by the celebrated Weyl character formula. However, such a formula does not hold in general for finite-dimensional irreducible modules over classical Lie superalgebras.
In this talk, we introduce an analogous conjectural character formula for finite-dimensional irreducible modules over classical Lie superalgebras, often referred to as Kac-Wakimoto formula, together with our recent work on the proof for the case of ortho-symplectic Lie superalgebras.
This is a joint work with Shun-Jen Cheng.

Speaker: 허석문 (성균관대)
Title: Hartshorne conjecture and vector bundles
Abstract: Hartshorne conjecture states that any smooth two codimensional subvariety in a projective space of dimension at least six is a complete intersection. It is checked to be equivalent to the statement that any vector bundle of rank two on a projective space of dimension at least six splits. It is also equivalent to another statement in terms of multiple structured Cohen-Macaulay schemes of degree two and three. For the last five years, we investigate vector bundles on some special varieties and their multiple structures. In this talk we report our recent results.

Speaker: 강현석 (GIST)
Title: Geometry of hypersurfaces evolved by curvature
Abstract: The evolution of hypersurfaces by curvature brought attention after it has been used to prove some well know problems, such as Willmore conjecture, not to mention the success of closely related Ricci flow in proving the geometrisation conjecture. Nevertheless, this topic has interesting geometric aspects with various areas of mathematics involved. Among many, we introduce the differential harnack inequality to give bounds on curvature at different points on the hypersurface, and obtain the sufficient conditions to develop the known result further for the perturbed curvature flows.  The latter is a joint with Ki Ahm Lee.

Speaker: 최재유 (경북대)
Title: Symplectic quotient, instantons and the additive Deligne-Simpson problem
Abstract: The instanton spaces and the additive Deligne-Simpson problem can be formulated via symplectic quotients of vector spaces of quiver representations. We give a brief overview of these constructions and the related partition functions in physics literatures. These functions appear in the context of the Intriligator-Seiberg duality, i.e., a Coulomb-Higgs branch correspondence.

Speaker: 조진석 (부산교대)
Title: Volume conjecture in a nutshell
Abstract: After introducing the quantum invariants and the hyperbolic structures of knots, we will briefly survey the meaning of the volume conjecture.