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 2-143**.

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.)

There are other math events that go on in the Cambridge area: at MIT, we have the Undergraduate Math Association, as well as the Harvard-MIT Math Tournament. There's also Tea with Mathematicians; we'll update this site with the dates for when undergraduates are invited to attend. (Harvard also has weekly tea in its math department.)

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.

Organizers: Sanath Devalapurkar, Marisa Gaetz, Elizabeth Han,
Brice Huang, Ahaan Rungta, and
Henry Shackleton.

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

Date: April 18, 5:45 pm

Title: **Regenerating Codes**

Speaker: **Margalit Glasgow**

Error-correcting codes allow us to encode a message into a redundant codeword,
such that even when some of the symbols in the codeword are erased (or
changed), we can recover the original message. In regenerating codes, which are
often used in distributed storage, we care about recovering the full codeword.
For example, in Reed-Solomon codes that encode k-symbol messages, if any symbol
in the codeword is lost, we can recover that symbol exactly using polynomial
interpolation from any other k-symbols of the codeword. But what about if the
symbols are really large and stored in the cloud, and we don't have the
bandwidth to download k full symbols? Can we recover the lost symbol using less
information? (Spoiler: yes) Come learn how!

References:

- Repairing Reed-Solomon Codes. Venkatesan Guruswami and Mary Wootters. STOC 2016.
- Optimal repair of Reed-Solomon codes: Achieving the cut-set bound Itzhak Tamo, Min Ye, Alexander Barg 2017

Date: April 11, 5:45 pm

Title: **Smoothness Classes of Minkowski Sums**

Speaker: **Yonah Borns-Weil**

The Minkowski Sum of two sets is the set of all vector sums of elements in the
sets. Somewhat surprisingly, the sum two convex sets in the plane with
$C^{\infty}$ (infinitely differentiable) boundaries need not have $C^{\infty}$
boundary. However, the sum's boundary must be differentiable, and twice
differentiable, and even three times differentiable... In this talk, we'll
prove the astonishing ``cutoff" of just how smooth such a boundary must be. The
proof will use only introductory analysis techniques, and the worst-case
scenario will be perfectly simple and constructive.

Prerequisites: Basic (18.100 level) analysis.

Date: April 4, 5:45 pm

Title: **Dimensionality Reduction While Preserving Distances**

Speaker: **Sandeep Silwal**

Dimensionality reduction is an important tool in numerical linear algebra,
statistics, and algorithms. In this talk, we present a nice proof of the
Johnson Lindenstrauss lemma which allows us to reduce the size of vectors while
preserving their pairwise distances. We will also look at some applications of
this lemma to combinatorics and algorithms.

References:

- Sanjoy Dasgupta, Anupam Gupta: http://cseweb.ucsd.edu/~dasgupta/papers/jl.pdf.
- Paul Beame: https://courses.cs.washington.edu/courses/cse522/14sp/lectures/lect10.pdf.
- Dimitris Achlioptas: https://www.sciencedirect.com/science/article/pii/S0022000003000254.
- Noga Alon: http://www.tau.ac.il/~nogaa/PDFS/extremal1.pdf.
- Hu Ding: http://www.cse.msu.edu/~huding/selected/JL.pdf.

Date: March 14, 5:30 pm

Title: **Formulas for Pi**

Speaker: **Yang Liu**

Ramanujan proved many absurd formulas for pi. We explain how one would go about
deriving one of these formulas.

Date: March 7, 5:45 pm

Title: **The integral of $e^{x^2}$ (or lack thereof)**

Speaker: **Ashwin Sah**

We give a more or less complete proof of the classical and well-known, yet
rarely proven fact that e^{x^2} and other functions have no elementary
integrals.

**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.

If you would like to organize such math activities yourself, you can request room reservations in the Math Department HQ (next to Academic Services). (In particular, Barbara Peskin covers recurring, e.g. weekly, reservations. Make sure to specify room specifications, e.g. "flat, seats 30, tables and chairs, video projector". 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.)