Wow! What a fun week. Just wanted to say thanks again to Professor Brendan Hassett for coming out and spending the week teaching us all about Algebraic Geometry. For those who don’t know, Professor Hassett is a professor at Brown University and is the director of ICERM (which, if you are an undergraduate reading this, you should definitely apply to!)
To recap, the distinguished lecture series is an annual event in the BC math department, and it is one of our biggest events of the year. It is a series of 3 lectures given by a distinguished lecturer who is chosen and invited by the faculty. One of the best parts of the series is how it aims to be accessible to all audiences–the first lecture is designed for a general audience, and then the lectures get more specialized over the next few days, culminating in a talk about current research. Here’s a list of the abstracts from this past week:
Wed, March 22, 4pm at McGuinn 121
(For general audience) – Refreshments: 3:45 PM
Title: Parametrizing solutions to equations
Abstract: When can we write down all the solutions of a polynomial equation? We seek equations that can be parametrized with rational functions. These are used in mapmaking (stereographic projection), computer graphics, and modeling problems. Indeed, parametrizations are often the most efficient way to render geometric objects as screen images. Mathematicians have developed a rich theory for determining when such parametrizations are possible.
Thu, March 23, 4pm at Higgins 300
Title: Criteria for rationality
Abstract: It is a fundamental challenge to find parametrizations for the solutions of a polynomial equation–or demonstrate that such a parametrization is impossible. The underlying varieties are said to be rational or irrational respectively. We survey criteria for rational varieties, starting from Riemann’s definition of the genus of an algebraic curve in the 1850’s. These mix ideas from complex analysis, topology, and algebra. Despite this extensive toolbox, basic questions remain open: Are there irrational cubic fourfolds? Rational quartic hypersurfaces?
Fri, March 24, 4pm at Maloney 560
Title: Rationality and irrationality in families
Abstract: Can a family of smooth projective complex varieties have both rational and irrational members? We present four-dimensional examples showing this may occur. This builds on recent advances by Claire Voisin and others, employing decompositions of the diagonal, deformation theory, and Galois cohomology to detect irrationality. (joint with Pirutka and Tschinkel)
So, thanks again for everyone for coming out and welcoming Professor Hassett to BC. The talks were all very exciting and everyone I’ve talked to walked away with something new that they learned. If you missed the lectures this year, this event is something to keep an eye out for next year. And as always, we have some more events planned for you for the rest of the semester (block party on Monday!!).
