Founded in March 2014, the SCUM is a series of weekly math talks/panels by (mostly) undergraduates, for undergraduates, at MIT. Anyone is invited to speak about a math topic he or she finds interesting, sometimes but usually not original research, and talks are open to the MIT community (as well as interested visitors, e.g. from Harvard). With the support of the MIT Mathematics Department (and in past semesters, the Undergraduate Mathematics Association (UMA), Undergraduate Society of Women in Math (USWIM), and the Harvard-MIT Mathematics Tournament), SCUM also features free dinner each week! We'll meet weekly on **Wednesdays, 5:30--6:30 PM, in room 4-145**.

If you are interested in picking up a talk, please send a title and abstract, as well as any appropriate references (optional but recommended), to scum-exec@mit.edu. (If you have any food preferences, let us know!) In addition, please include a preference for dates, and any other accommodations you will need (e.g. projector). Talks should be fifty minutes long and accessible to first-year undergraduate math majors. We strongly recommend attending several SCUM talks before signing up to give one yourself.

(For logistical tips/advice on organizing such activities yourself, see below here.)

To receive email announcements, make sure you are either a declared MIT math major (which by definition excludes all freshmen first semester), or on the scum-interest mailing list (possibly via UMA or USWIM). If you do not have MIT certificates, email scum-exec@mit.edu and we'll manually add you to the mailing list.

Alternatively, you can like or follow us on Facebook at https://www.facebook.com/colloquium18/

Organizers: Ahaan Rungta, Sandeep Silwal, Victor Wang, and possibly others to be determined (definitely let us know if you're interested!)

**Meeting Time/Place**: Wednesdays, 5:30 PM, in 4-145

**Let us know if you (or someone you know) might like to give a talk**, or if you have suggestions for topics/ideas you would like to see in future talks.

See the archive here.

Date: Tuesday, 16 May at 5:55 PM in 56-154

Title: **Julia Robinson and Hilbert's Tenth Problem**

Speaker: **HDMI**

Abstract: SCUM will host a screening (and discussion as time permits) of the ~1 hour documentary "Julia Robinson and Hilbert's Tenth Problem" documenting Julia Robinson and her role in the resolution of the famous https://en.wikipedia.org/wiki/Hilbert%27s_tenth_problem over the integers*, which lies at the intersection of logic and number theory.

*Other natural extensions remain open; see Poonen's articles below.

Further reading for those interested:

- "Julia Robinson and Hilbert's Tenth Problem", http://zalafilms.com/films/juliarobinson.html or http://mit.kanopystreaming.com/video/julia-robinson-and-hilbert-s-tenth-problem
- Film review, http://www.ams.org/notices/200805/tx080500573p.pdf
- Poonen, "Undecidability in number theory", http://www-math.mit.edu/~poonen/papers/h10_notices.pdf
- Poonen, "Hilbert's Tenth Problem and Mazur's Conjecture for large subrings of Q", http://math.mit.edu/~poonen/papers/subrings.pdf

Date: Monday, 01 May at 5:45 PM in 56-114

Title: **Counting from infinity**

Speaker: **HDMI** (inspired by Mark Sellke)

Abstract: SCUM will host a screening (and discussion as time permits) of the ~1 hour documentary "Counting from infinity" documenting Yitang Zhang's prime gaps breakthrough from a couple years ago.

Further reading for those interested:

- "Counting from infinity", http://www.zalafilms.com/films/countingindex.html
- https://www.quantamagazine.org/20130519-unheralded-mathematician-bridges-the-prime-gap/
- https://www.quantamagazine.org/20131119-together-and-alone-closing-the-prime-gap/
- http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty

Date: Wednesday, 12 April

Title: **Simplicial Sets**

Speaker: **Attilio Castano**

Abstract: In rough terms, a simplicial set is a “space" built by pasting together n-dimensional triangles. While at first exposure the definition of a simplicial sets may look nothing like a space, I hope that I can motivate why it is a natural definition to have. For this I will introduce the notion of a presheaf. Given a small category C, one can interpret C as the category of building objects, and the presheaf category Pre(C) as the category of built objects. In this way we will see that the category of simplicial sets is just the category of built objects of the category of n-dimensional triangles.

Prereqs: Some familiarity with basic category theory (categories, functors, natural transformations, and colimits) could be useful, but I'll try to introduce what we will need, although my definitions may be a bit hand wavy for accessibility sake. You should still come, I have explained simplicial sets to non math majors before with some success.

Further reading if interested:

- I wrote an expository paper during the summer, and the lecture will be based on Chapter 1 here: http://www.mit.edu/~aecm93/UHT.pdf
- To write this chapter I learned the material mainly from Daniel Duggers - Sheafs and homotopy theory: http://pages.uoregon.edu/ddugger/cech.html
- Emily Riehl - A leisurely introduction to simplicial sets: http://www.math.jhu.edu/~eriehl/ssets.pdf

Date: Wednesday, 01 March

Title: **When can preferences be aggregated?** ("The topological approach to social choice")

Speaker: **Jeremy Owen** (G1 in physics)

Abstract: In many instances, one might wish to aggregate the preferences of many individuals, for example, in order to guide a collective decision. When is this possible? In the 1980s, G. Chichilnisky used algebraic topology to answer this and related questions, continuing the tradition of topology shedding light on economics (previously, most famously in the form of various fixed point theorems). My talk will sketch this exciting approach to social choice problems, explaining in particular: (i) how one models preferences and their aggregation in the topological framework, and (ii) under what conditions fair social choice is possible.

Prereqs: The arguments will depend on some group theory and algebraic topology, but the structure of the ideas presented will be accessible to a broader audience.

Further reading if interested:

- B. Eckmann, Social Choice and Topology A Case of Pure and Applied Mathematics Expo. Math. 22 (2004), 385-393.
- Who cares about topology? (Inscribed rectangle problem), 3Blue1Brown, https://youtu.be/AmgkSdhK4K8

Date: Wednesday, 15 February

Title: **Applications of Expander Graphs**

Speaker: **Yang Liu**

Abstract: Expanders are both interesting in combinatorics and have interesting applications in Theoretical Computer Science. First, we give several equivalent definitions of expanders and then explain the existence of expanders and give explicit constructions. Afterwards, we give several interesting algorithmic applications of expander graphs.

Prereqs: Spectral theorem for symmetric matrices (see http://web.mit.edu/jorloff/www/18.03-esg/notes/symmetricMatrices.pdf for instance), knowledge of algorithms (time and space, randomized algorithms).

Topics: Definition of expanders using edge expansion, vertex expansion, and spectral properties. Equivalence of definitions. Graph products preserving expansion. Undirected connectivity in logspace. Reducing random bits using expanders.

Further reading if interested:

- https://en.wikipedia.org/wiki/Expander_graph
- Computational Complexity: A Modern Approach
- "Undirected connectivity in log-space", http://dl.acm.org/citation.cfm?id=1391291
- https://www.cs.cmu.edu/~avrim/Randalgs97/lect0212 (notes from a class on Randomized Algorithms)

If you would like to organize such math activities yourself, you can request room reservations in the Math Department HQ (next to Academic Services). As of Fall 2016, one-time/individual room reservations can be made at classrooms.mit.edu. Also, currently Dr. Barbara Peskin (academic administrator)covers recurring, e.g. weekly, reservations. Make sure to specify room specifications, e.g. "flat, seats 30, tables and chairs, video projector". (For recurring reservations, it is difficult to request specific rooms, so instead it is probably wise to request to *not* have certain bad rooms.) You can also probably easily find out the right people to ask for logistical things like funding or term-to-term seminar-listing adjustments; email us if you have questions.

Food-related: MIT students do not need to pay tax (see here for tax exemption forms). One convenient option is to set up a tax-exempt account on Foodler, as described in their FAQ. (You can often request plates, utensils, cups, and napkins. Drinks are often cheaper separately, e.g. at convenience stores.)