Difference between revisions of "NTS ABSTRACT"

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Group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of representations of the group. In particular, the representations of small dimension tend to contribute the largest terms to these sums, so a systematic knowledge of these small representations could lead to proofs of some of these facts. This talk will discuss a new method for systematically constructing the small representations of finite classical groups. I will explain the method with concrete examples and applications. This is part from a joint project with Roger Howe (Yale).
 
Group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of representations of the group. In particular, the representations of small dimension tend to contribute the largest terms to these sums, so a systematic knowledge of these small representations could lead to proofs of some of these facts. This talk will discuss a new method for systematically constructing the small representations of finite classical groups. I will explain the method with concrete examples and applications. This is part from a joint project with Roger Howe (Yale).
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== Feb 18 ==
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| bgcolor="#BCD2EE"  align="center" | ''Conductors and minimal discriminants of hyperelliptic curves with rational Weierstrass points''
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Conductors and minimal discriminants are two measures of degeneracy of the singular fiber in a family of hyperelliptic curves.  In the case of elliptic curves, the Ogg-Saito formula shows that (the negative of) the Artin conductor equals the minimal discriminant.  In the case of genus two curves, equality no longer holds in general, but the two invariants are related by an inequality.  We investigate the relation between these two invariants for hyperelliptic curves of arbitrary genus.
 
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Revision as of 16:23, 11 January 2016

Return to NTS Spring 2016

Feb 04

Shamgar Gurevich
Low Dimensional Representations of Finite Classical Groups

Group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of representations of the group. In particular, the representations of small dimension tend to contribute the largest terms to these sums, so a systematic knowledge of these small representations could lead to proofs of some of these facts. This talk will discuss a new method for systematically constructing the small representations of finite classical groups. I will explain the method with concrete examples and applications. This is part from a joint project with Roger Howe (Yale).


Feb 18

Padmavathi Srinivasan
Conductors and minimal discriminants of hyperelliptic curves with rational Weierstrass points

Conductors and minimal discriminants are two measures of degeneracy of the singular fiber in a family of hyperelliptic curves. In the case of elliptic curves, the Ogg-Saito formula shows that (the negative of) the Artin conductor equals the minimal discriminant. In the case of genus two curves, equality no longer holds in general, but the two invariants are related by an inequality. We investigate the relation between these two invariants for hyperelliptic curves of arbitrary genus.