Harvard University Math Department

Talk begins at 4:30, reception begins at 5:30, snacks provided.

**Speaker:**Moon Duchin (Tufts)**Title:**Random Everything**Abstract:**Random processes and random constructions are all over math, and have many applications as well. I'll give a tour of some highlights of randomness in math, from number theory to geometry, plus applications to politics if I have time.

**Speaker:**Matt Parker (Standup Maths and Queen Mary University of London)**Title:**Stand-up Math: using performance to engage people with mathematics

**Speaker:**Bena Tshishiku (Harvard)**Title:**The odd thing about car sunshades**Abstract:**There's something magical about the Magic Shade (https://www.youtube.com/watch?v=LN65aQsKnMo). It has to do with topology, group theory, and the mathematics of braids and links.

**Speaker:**Glen Whitney (Studio Infinity and Harvard)**Title:**Double Double, Dual Trouble: a twisted tale of geometry**Abstract:**The five Platonic solids have attracted mathematical interest for centuries, and one fruitful way to think of them is as two pairs of dual polyhedra and one polyhedron that is dual to itself. Roughly, two polyhedra are dual to each other if the faces of one correspond to the vertices of the other, and vice versa. There are numerous ways to make that concept mathematically precise in the case of highly symmetric polyhedra like the Platonic solids, but as we'll see, those different approaches have surprisingly different consequences when we try to extend the notion of "dual" to larger classes of polyhedra.

**Speaker:**Laure Flapan (Northeastern)**Title:**The Luroth problem: algebraic curves, field extensions, and beyond**Abstract:**The Luroth theorem describes when a complex algebraic curve, meaning a real surface given by polynomial equations, is topologically a sphere. In this talk we will discuss how this problem may be translated into a seemingly completely different problem about algebra. In this talk we’ll discuss the proof of theorem, some generalizations to higher dimensions, and some related long-standing open questions in algebraic geometry.

**Speaker:**Noam Elkies (Harvard)**Title:**Mathematical Tree-Planting**Abstract:**If nine trees be planted in a plane field, how many straight rows of three trees can be formed? This puzzle was once credited to Newton; while that attribution is surely spurious, such "points and lines" puzzles do have a history going back at least to the early 1800's, and continue to provide an accessible point of entry into several branches of mathematics -- from elementary geometry and linear algebra to additive number theory and modern algebraic geometry -- and many open problems. We introduce some of these ideas and questions, and report on some classical and recent results.

**Mailing list:** You can subscribe to the seminar mailing list here.

**Organizers:** Ana Balibanu (ana@math.harvard.edu) and Alison Miller (abmiller@math.harvard.edu)