Tata Institute of Fundamental Research
Winding Line on a Torus
Student Seminar
Speaker:
Sudarshan Gurjar
School of Mathematics
Tata Institute of Fundamental Research
Homi Bhabha Road
Mumbai 400005
Date:
Friday, 11 Sep 2009 (all day)
Venue:
A-212 (STCS Seminar Room)
(Scan to add to calendar)
Abstract:
The torus is one of the most important geometrical objects in mathematics. As a topological space it is just a product of two circles. The is a natural continuous mapping from the real plane to the torus which is called the exponential map. It is of interest to understand the image of a line through the origin in the plane in the torus under the exponential map. If the line has irrational slope its image in the torus is dense, that is it approaches every point arbitrarily closely. If time permits few more facts about the winding line will be mentioned.
| Speaker: | Sudarshan Gurjar School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road Mumbai 400005 |
| Date: | Friday, 11 Sep 2009 (all day) |
| Venue: | A-212 (STCS Seminar Room) |
(Scan to add to calendar)
Abstract:
The torus is one of the most important geometrical objects in mathematics. As a topological space it is just a product of two circles. The is a natural continuous mapping from the real plane to the torus which is called the exponential map. It is of interest to understand the image of a line through the origin in the plane in the torus under the exponential map. If the line has irrational slope its image in the torus is dense, that is it approaches every point arbitrarily closely. If time permits few more facts about the winding line will be mentioned.