An intertwine of two graphs G and H is a graph that has both G and H as a minor and is minor-minimal with this property. In 1979, Lovász and Unger conjectured that for any two graphs G and H, there are only a finite number of intertwines. This now follows from the graph minors project of Robertson and Seymour, although no ‘elementary’ proof is known.
In this talk, we consider intertwining problems for matroids. Bonin proved that there are matroids M and N that have infinitely many intertwines. However, it is conjectured that if M and N are both representable over a fixed finite field, then there are only finitely many intertwines. We prove a weak version of this conjecture where we intertwine ‘connectivities’ instead of minors. No knowledge of matroid theory will be assumed.
This is joint work with Bert Gerards (CWI, Amsterdam) and Stefan van Zwam (Princeton University).

We propose a new EIT image reconstruction algorithm using multiple
boundary voltage data from a planar array of voltage-sensing electrodes. The current
injection electrodes are placed so that the induced internal currents approximately
flow in the direction parallel to the surface of the voltage-sensing probe. The proposed
algorithm uses the interrelationship between the measured voltage differences and the
computed current, which allows us to derive a PDE-based Ohms law. Based on the
derived voltage-current relation, we produce images of admittivity changes within
a local region underneath the voltage-sensing probe. We describe the new image
reconstruction algorithm and its numerical simulation results.

We introduce a new invariant called the slope invariant
for all tunnels for tunnel number one knots in the 3-sphere, arising
from a study of the disk complex of the standard genus two handlebody
in the 3-sphere. The slope invariants have been calculated for some
well known tunnels, including all tunnels for 2-bridge knots and torus
knots, and all (1, 1)―tunnels. We introduce briefly a way to calculate
them, and their several applications in other related topics.

The study of vortex rings in incompressible 3D fluids dates back to Kelvin and Helmholtz in the mid 1800's. In 1906, Da Rios and Levi-Civita gave a formal derivation of a geometric flow for filaments of infinitely small cross section and arbitrary shape. This flow is now widely called the binormal curvature flow. In the talk, I will first review and then present recent results on stability estimates for the filament flow, and their application to so-called Schrodinger maps. 

It has been known for more than 20 years that certain semilinear
parabolic equations, such as the Allen-Cahn equation, exhibit interfaces that, in certainlimits, evolve by the mean curvature flow, a parabolic geometric evolution. We prove some analogous results relating semilinear hyperbolic
equations and certain hyperbolic geometric evolution problems.

Braids are beautiful objects in low dimensional topology. They can be seen likewise as tangles in the 3-ball or as elements of the mapping class group of the punctured disc or as automorphisms of free groups.We start by recalling the construction of the HOMFLYPT invariant for tangles , the Niesen-Thurston classification of diffeomorphisms of the punctured disc and the growth rate of  automorphisms of  free groups.
We present then our machinery for constructing 1-cocycles which produce HOMFLYPT invariants for 1-parameter families of tangles. It turns out that they contain information about the geometry of braids. There will be lots of examples in the talk.

We construct easily calculable invariants for tangles which can distinguish mutants without using cabling operations. They refine the HOMFLYPT and the 2-variable Kauffman invariant and they are no longer multiplicative under the composition of tangles.

As a first geometric application we show that the invariants can detect that a given braid is not isotopic to a rotation of the disc. We conjecture that they are a complete invariant for the geometric type of braids.

Imagine that you are cooking chicken at a party. You will cut the raw chicken fillet with a sharp knife, marinate each of the pieces in a spicy sauce and then fry the pieces. The surface of each piece will be crispy and spicy. Can you cut the chicken so that all your guests get the same amount of crispy crust and the same amount of chicken?
We show that if the number of guests is a prime power, n=p^k. Then such partition is possible. We derive this from a more general statement about equipartitions of convex bodies with respect to a measure and d-1 continuous functionals on the space of convex bodies, where d is the dimension the convex body sits in.
Our proof uses optimal transport and equivariant topology.

We construct easily calculable invariants for tangles which can distinguish mutants without using cabling operations. They refine the HOMFLYPT and the 2-variable Kauffman invariant and they are no longer multiplicative under the composition of tangles.

As a first geometric application we show that the invariants can detect that a given braid is not isotopic to a rotation of the disc. We conjecture that they are a complete invariant for the geometric type of braids.

In this introductory seminar, we first introduce the concept of "Quality of Service Guarantee"
that is important in the design of communication networks. We then investigate how to implement the concept in real communcation networks and what is the role of teletraffic theory in this regard.

We construct easily calculable invariants for tangles which can distinguish mutants without using cabling operations. They refine the HOMFLYPT and the 2-variable Kauffman invariant and they are no longer multiplicative under the composition of tangles.

As a first geometric application we show that the invariants can detect that a given braid is not isotopic to a rotation of the disc. We conjecture that they are a complete invariant for the geometric type of braids.

In the 1970s, Lovász and Plummer conjectured that every cubic bridgeless graph has exponentially many perfect matchings. This was proven by Voorhoeve for bipartite graphs and by Chudnovsky and Seymour for planar graphs. In this talk I will describe our proof of the general case, which uses elements of both aforementioned partial results as well as Edmonds’ characterization of the perfect matching polytope.
(Joint work with Louis Esperet, František Kardoš, Daniel Král’, and Sergey Norin.)

Shadow systems are often used to approximate
reaction–diffusion systems when one of the diffusion rates is large.
In this talk, we focus on the global existence and blow-up phenomena
for shadow systems. Our results show that even for these fundamental
aspects, there are serious discrepancies between the dynamics of the
reaction–diffusion systems and that of their corresponding shadow systems.

Based on Korea’s experience, this talk discusses issues related in massive capital inflows in emerging market countries and hopefully draws policy lessons for Asia and Pacific countries dealing with capital inflows problem.

Based on Korea’s experience, this talk discusses issues related in massive capital inflows in emerging market countries and hopefully draws policy lessons for Asia and Pacific countries dealing with capital inflows problem.

In this talk, we will discuss on the uniqueness for the Radon transform.

Our first problem is the global uniqueness.

It is interesting that the global uniqueness does not hold without any global decay condition on the function.

Our next problem is the uniqueness in the exterior problem. In this problem, it is well-known that it is essential to assume the rapid decay condition on the function.

In this talk, however, there is another essential condition on this problem.

Throughout these problems, we claim the importance the singularities of the function at infinity.

TBA

In this talk I will talk about the inviscid limit of Bejamin-Ono-Burgers (BOB) equation.  We prove that the Cauchy problem for the BOB equation is uniformly (with respect to the viscid parameter) globally well-posed in $H^s$ ($s\geq 1$) for all. Moreover, we show that the solution converges to that of Benjamin-Ono equation in $C([0,T]:H^s)$ ($s\geq 1$) for any $T>0$ as $\ve\to 0$. Our results give a new proof without gauge tranform for the global wellposedness of BO equation in $H^1$ which was first obtained by Tao \cite{TaoBO}, and obtain the inviscid limit behavior in $H^1$.

TBA

The Koszul complex is perhaps the most important complex in
commutative algebra. Its most striking features are its algebra
structure, its grade-sensitivity and its relations with syzygies.
Koszul cycles and homology themselves have an algebra structure. In a
regular local ring or in a polynomial ring the Koszul complex of the
maximal (homogeneous) ideal gives a resolution of the residue field.
In a non-regular ring the residue field has an infinite resolution
(which has also an algebra structure) "containing" the Koszul complex.
Commutative Koszul algebras are graded algebras whose residue field
has a free resolution which has a property in common with the Koszul
complex: it is linear. Here linear means that the matrices describing
the maps in the resolution have entries of degree 1. Koszul algebras
have several important properties. For certain homological aspects
they behave like polynomial rings, for other like complete
intersections. The main goal of the talks will be discuss these
features of Koszul algebras, their syzygies and bounds on the
regularity of Koszul homology in general. I will also present several
combinatorial/algebraic methods for proving that an algebra is Koszul
with some application to Veronese varieties and their projections.

I will present a new weighted voting classification ensemble method that uses two weight vectors: a weight vector of classifiers and a weight vector of instances.  The instance weight vector assigns higher weights to observations that are hard to classify.  The weight vector of classifiers puts larger weights to classifiers that perform better on hard-to classify instances. One weight vector is designed to be calculated in conjunction with the other through an iterative procedure. We proved that the iterated weight vectors converge to the optimal weights which can be directly calculated from the performance matrix of classifiers in an ensemble. The final prediction of the ensemble is obtained by the voting using the optimal weight vector of classifiers.  To compare the performance between a simple majority voting and the proposed weighted voting, we applied both of the voting methods to bootstrap aggregation and investigated the performance on 28 data sets. The result shows that the proposed weighted voting performs significantly better than the simple majority voting in general.

Abstract: Since the inception of gauge theory - Donaldson theory and Seiberg-Witten theory - in late 20 century, a mystery of smooth 4-manifolds has been unveiled and studying 4-manifolds has been the most active and central research area in geometry and topology. 
   One of the fundamental problems in smooth 4-manifolds is to classify simply connected smooth and symplectic 4-manifolds. Topologists and geometers working on 4-manifolds have obtained many fruitful and striking results in this direction in last 30 years. 
   In this lecture series I'd like to review briefly some classical invariants of 4-manifolds and Seiberg-Witten theory with applications. And then, I'll survey various constructions of smooth 4-manifolds such as a logarithmic transform, fiber-sum and a knot surgery. Especially I'll review a knot surgery in some details which turned out to be a powerful tool in the study of smooth 4-manifolds.

Raviart-Thomas finite elements are very useful for problems
posed in H(div) since they are H(div)-conforming. We introduce two
domain decomposition methods for solving vector field problems posed
in H(div) discretized by Raviart-Thomas finite elements. A two-level
overlapping Schwarz method is developed. The coarse part of the
preconditioner is based on energy-minimizing extensions and the local
parts consist of traditional solvers on overlapping subdomains. We
also consider a balancing domain decomposition by constraints (BDDC)
method. The BDDC preconditioner consists of a coarse part involving
primal constraints across the interface between subdomains and local
parts related to the Schur complements corresponding to the local
subdomain problems.