In the complex projective plane, how many degree d rational curves pass through 3d - 1 given points in general position? The answers N_d to this question for d = 1,2,3,4 were known classically, but on... More

Any compact irreducible 3-manifold admits a decomposition (JSJ decomposition) into pieces which are either Seifert fibered or Atoroidal. Waldhausen studied and classified manifolds where the JSJ decom... More

In the complex projective plane, how many degree d rational curves pass through 3d - 1 given points in general position? The answers N_d to this question for d = 1,2,3,4 were known classically, but on... More

We will present a proposed proof of the Andrews-Curtis Conjecture.

In the complex projective plane, how many degree d rational curves pass through 3d - 1 given points in general position? The answers N_d to this question for d = 1,2,3,4 were known classically, but on... More

It is known that the category of Waldhausen categories is a closed symmetric multicategory and algebraic K-theory is a functor from the category of Waldhausen categories to the category of spectra. By... More

We will provide more details about the construction of Stark-Heegner/Darmon points on elliptic curves over arbitrary number fields that was discussed in our talk last Fall.

Let M, N be finite-dimensional manifolds with M compact. In this talk I

will look at the Riemnannian geometry on the space C^\infty(M,N) of

smooth maps equipped with the L^2-Riemannian m... More

K-theory is a very large, useful subject with applications in many areas of mathematics. Vaguely speaking, it is very useful for classifying invariants and it can also be seen as a generalization of l... More

K-theory is a very large, useful subject with applications in many areas of mathematics. Vaguely speaking, it is very useful for classifying invariants and it can also be seen as a generalization of l... More

We present a general method to compute a presentation for any cusped hyperbolic lattice Gamma, applying a classical result of Macbeath to a suitable Gamma-invariant horoball cover of the corresponding... More

K-theory is a very large, useful subject with applications in many areas of mathematics. Vaguely speaking, it is very useful for classifying invariants and it can also be seen as a generalization of... More

Various generalizations of the octonions will be presented, and difficulties that arise in higher dimension explored. In particular, any two octonions generate a quaternionic sub algebra. However, th... More

A subset W of a Manifold M is k-contractible if the inclusion factors homotopically through k, where k is a cw-complex of dimension lower then M. The k-category of a manifold is the smallest number o... More

Various generalizations of the octonions will be presented, and difficulties that arise in higher dimension explored. In particular, any two octonions generate a quaternionic sub algebra. However, th... More

In this talk I will introduce some the basic concepts in the study of the qualitative theory of



dynamical systems. After that I will move into the setting of discrete dynamical system ... More

In this talk I will give a brief summary of the relation between some interesting characteristic classes and geometry invariants for projective varieties.

We will review the octonion algebra, including how to use it to define a parallelization of S^7. We will then proceed to show that an octonion valued function as a point can be recovered by an integra... More

In this talk I will give a brief summary of the relation between some interesting characteristic classes and geometry invariants for projective varieties.

We derive new equations for the idealized motion of a flag on a pole in 3-space, viewed as an unstretchable piece of fabric with no friction and ignoring self-collisions. Geometrically the flag repres... More

One way to define a central extension of simplicial groups is by saying it a short exact sequence of simplicial groups so that level-wise it is a central extension of groups. From this definition we w... More

One way to define a central extension of simplicial groups is by saying it a short exact sequence of simplicial groups so that level-wise it is a central extension of groups. From this definition we w... More

In this talk I will describe certain algebraic structures related to Matroid Theory. After defining a matroid over a ring, I will focus on matroids over a field k

and matroids over the integers... More