news

Math Community Web Page

Following up on the #shutdownSTEM discussions, the Department of Mathematics has launched a community web page, with evolving content to be created through community effort.
Read more

#shutdownSTEM–10 June 2020

In partnership with the Harvard Division of Science, the Mathematics Department used the call to #shutdownSTEM on 10 June to initiate a discussion of actions...
Read more

See Older News

announcements

upcoming events

< 2018 >
December
«
»
Sun
Mon
Tue
Wed
Thu
Fri
Sat
November
November
November
November
November
November
1
2
3
4
5
6
7
  • Irreducible SL(2,C)-representations of homology-3-spheres
    3:30 PM-4:30 PM
    December 7, 2018
    1 Oxford Street, Cambridge, MA 02138 USA
    Abstract:

    We prove that the splicing of any two non-trivial knots in the 3-sphere admits an irreducible SU(2)-representation of its fundamental group. This uses instanton gauge theory, and in particular a non-vanishing result of Kronheimer-Mrowka and some new results that we establish for holonomy perturbations of the ASD equation. Using a result of Boileau, Rubinstein, and Wang (which builds on the geometrization theorem of 3-manifolds), it follows that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL(2,C).

8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
January
January
January
January
January