# NIU Department of Mathematical Sciences

# Upcoming Colloquia and Seminars

### Math Department Colloquium

**Friday, March 27**, 4:00-5:00 p.m. in DU 348

Speaker:

**Christopher Drupieski**, DePaul Univ.

Title:

*Cohomology and Geometry for Groups and Related Structures*

**Abstract:**It has been known since the publication of Maschke's Theorem in 1899 that, over a field of characteristic zero, every finite-dimensional representation of a finite group G decomposes into a direct sum of irreducible representations. On the other hand, over a field k of prime characteristic dividing the order of G (the modular situation), there are non-split extensions between kG-modules. These non-split extensions are parameterized, up to equivalence, by certain cohomology spaces. In the past 30 years, much progress has been made studying cohomology spaces for finite groups, restricted Lie algebras, and related algebraic structures by way of certain associated geometric invariants, called (cohomological) support varieties. In this talk I will give an overview of some of the big results and methods in this area. I will then hint at some of my recent work studying the cohomology of finite supergroup schemes.

### Seminars

Algebra Seminar: | Wednesday, Mar. 25 , 4:15-5:15 p.m. in DU 378 | |

Speaker: | Mike Geline | |

Topic: | Introduction to Representation Theory and Brauer's
Induction Theorem
| |

Abstract: | This seminar series will be aimed at graduate students, and will constitute an informal (but hopefully informative) course on representations of finite dimensional algebras with an emphasis on representations of finite groups. We will begin with a (hopefully brief) review of semisimplicity and the distinction between irreducible (versus absolutely irreducible) modules. We'll define characters early as well. Then we'll define the ubiquitous concept of induced representations (and induced characters) with the aim of proving a fascinating and powerful result known as Brauer's induction theorem (or if time permits one of its stronger variations). Brauer's theorem began life as a conjecture of Emil Artin, who anticipated an application to L-functions attached to representations of Galois groups. But it turned out to have many applications to group theory as well, and also quite surprisingly to certain questions in algebraic topology. |

Complex Analysis Seminar: | Tuesday, Mar. 31, 11:00-11:50 p.m. in DuSable 464 | |

Speaker: | Alastair Fletcher | |

Topic: | Fixed curves near fixed points
| |

Abstract: | We will discuss the behaviour of certain quasiregular mappings in the plane near fixed points. In particular, we will show how to count the numbers of fixed external curves which land at the fixed point. This will be an overview of how things work, and will take in topics including complex dynamics, circle endomorphisms and Blaschke products. |

Applied Math Seminar: | Tuesday, Mar. 24, 11:30-12:20 p.m. in Watson 110 | |

Speaker: | Nathan Krislock | |

Topic: | Semidefinite Optimization and Combinatorial Optimization
| |

Abstract: | During the last two decades, semidefinite optimization has grown into a significant field of research with applications in many diverse areas such as graph theory, distance geometry, combinatorial optimization, low-rank matrix completion, and polynomial optimization. In combinatorial optimization, semidefinite optimization is used to compute high-quality bounds to many difficult (in fact, NP-hard) problems, such as Max-Cut and maximum k-cluster. This has led to the development of state-of-the-art branch-and-bound methods for solving such problems to optimality. |