Title: Compact forms of spaces of constant negative (sectional) curvature.
Abstract: One knows that any compact riemann surface of genus > 2 carries
a riemanniann metric of constant curvature. In higher dimension even the
existence of compact manifolds of constant negative curvature is by no
means that abundant. In this lecture we will show how arithmetic enables us
to construct such manifolds in every dimension greater than equal to 2.
Title: The Hoskin-Deligne formula for the co-length of a complete ideal in
2-dimensional regular local ring.
Abstract: We shall present a simple proof due to Vijay Kodiyalam.
This proof makes use of the fact that transform of a complete ideal
in a two-dimensional regular local ring R in a quadratic transform of R
is again complete. It also uses a structure theorem, due to Abhyankar,
of two-dimensional regular local rings birationally dominating R.
4:00pm
5:00pm
6:00pm
Time:
3:00pm
Location:
Room 215
Description:
Title: Compact forms of spaces of constant negative (sectional) curvature.
Abstract: One knows that any compact riemann surface of genus > 2 carries
a riemanniann metric of constant curvature. In higher dimension even the
existence of compact manifolds of constant negative curvature is by no
means that abundant. In this lecture we will show how arithmetic enables us
to construct such manifolds in every dimension greater than equal to 2.
Time:
3:30pm-5:00pm
Location:
Ramanujan Hall
Description:
Title: The Hoskin-Deligne formula for the co-length of a complete ideal in
2-dimensional regular local ring.
Abstract: We shall present a simple proof due to Vijay Kodiyalam.
This proof makes use of the fact that transform of a complete ideal
in a two-dimensional regular local ring R in a quadratic transform of R
is again complete. It also uses a structure theorem, due to Abhyankar,
of two-dimensional regular local rings birationally dominating R.