Distinguished Lecture Series 2017

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!!).

Undergraduate Research (And First Post of the Semester)!

Thanks again for everyone for coming out to the research symposium last Monday, it was a ton of fun and it was a great way to kick off the semester.

Also many thanks to those who presented their research (Andre Wei, Arthur Diep-Nguyen, Chris Ratigan, and Champ Davis a.k.a. Me).

At the beginning of the event, we also talked about how to get involved with undergraduate research.  If you are interested, a great way to get started is to first talk to your current math professor.  You can also talk to either Professor Fedorchuk or Professor Keane.  Another great starting point is to visit this page on the BC math website.  Most people at BC do either an REU at a different school (usually funded by the NSF) or stay at BC and do a URF– hopefully I can make a more in depth post about undergrad research, but for now this is all I have to say.

Finally, we have many more exciting events planned for this summer, so stay tuned!  (also hopefully many more exciting blog posts)

Putnam 12/03/16

Just wanted to give a quick shoutout to everyone who took the Putnam this past Saturday.  We met in Maloney 536 at 10:00 am since we couldn’t use 560 or the lounge because of a topology seminar.  We don’t know if they were actually using the lounge though, because when we checked, the only thing there was a pile of bagels on the table with a note that said: “for the topology seminar (i.e. NOT FOR PUTNAM!)”

😦

That’s fine, we had our own bagels anyway.  And donuts.

Anyway, the test wasn’t bad, and I think we scored fairly well as a team.  As a whole, we did well on the first section (I think everyone got problems 1, 2, or both), but I think we agreed that the second section was more challenging (lots of analysis!).  The test ended at 6:00 pm–so in total, a great way to spend a Saturday.

And now we wait until the spring to get our results.

Here‘s a list / discussion of problems that were on the test:

Putnam Archive

Movie Night!

Just wanted to do a quick recap of our movie night that we had a couple days ago, which as you can imagine, was awesome.  As per Chris’s recommendation, we watched the documentary Julia Robinson and Hilbert’s Tenth Problem, which chronicles the life of the American mathematician Julia Robinson who made great progress towards the solution of Hilbert’s Tenth Problem (which led to its eventual solution by the Russian mathematician Yuri Matiyasevich).  It was also cool to see how Robinson pushed the boundaries and paved the way for women in mathematics.  I highly recommend watching it!  (it’s available to stream for free on BC’s library website).

Also, after the movie was over, we had an informal Q&A session with some current math majors / double majors on classes, life as a double major, studying abroad, etc.

So, if you have any questions about double majoring, feel free to ask these guys:

Andrew Ferdowsian (math/econ), Andre Wei (math/cs), Chris Ratigan, Christian Cofoid (math/finance)

Block Party!

Thanks everybody for coming to the block party yesterday!  We had a lot of pizza, but I think we had even more fun!  It was great hearing about how how everyone’s semesters are going (especially those in Algebra I/Analysis I), and it was great hearing everyone’s plans for next semester.

There are some awesome courses being offered next semester that I encourage everyone to check out:

MATH4440: Dynamical Systems – Prof. Mirollo

MATH4480 (1): Topics in Statistics – Prof. Baglivo

MATH4480 (2):  Mathematical Logic – Prof. Reed

CSCI3381: Cryptography – Prof. Straubing

All of these classes will surely be amazing!

See you at the movie night! (this Saturday, 6:15pm, Higgins 310, Julia Robinson and Hilbert’s Tenth Problem)

So… how many votes do you need?

Recently I flipped through a book by Frank Morgan called “The Math Chat Book,” which includes a bunch of fun, conversational math problems.  One of them was particularly interesting, given that election day is…. tomorrow!

Here is the question: What is the fewest number of votes with which you could be elected President of the United States?  (Assuming two candidates and about half of the population in each state votes).

For a brief history of popular vote statistics, the lowest percentage ever by an elected president was John Quincy Adams in 1824 with 30.9% of the popular vote (he actually lost the popular vote to Andrew Jackson, neither won the majority of the electoral votes, and the election had to be decided by the House of Representatives).  The highest ever was Warren Harding in 1920 with 60.3%.  Most presidents seem to get between 48-55% of the popular vote.

Now, to answer the question of the lowest possible…  The strategy is to win half the votes in states with about half the electoral votes.  So… about 25% of the popular vote.  Morgan says you can do even better since smaller states get more electoral votes per resident: just win 39 small states and the District of Columbia and you’d only need about 22% of the popular vote.

The whole situation changes if there are three candidates.  In fact, you can win it with less than 0.1% of the popular vote!  All you have to do is win Wyoming and have the other two candidates split the rest of the states so no one has a majority of electoral votes.  In that case the House of Representatives chooses the winner, you of course!!

I asked Chris Ratigan what he thought about this question, but I forgot to include the “half the population in each state votes” assumption.  So… his answer was that all you’d have to do is have a total of one person vote in the largest 9 or so states (until you get to 270), and then you’d win the presidential election with a grand total of 9 votes…

So if I could just get the 9 people who read this post to go vote for me, I could become president!

The Math Chat Book by Frank Morgan

Interesting NPR article

CGP Grey Video

Wednesday Math in Maloney

If you’re looking for a good day to come to the 5th floor of Maloney, then try any day of the week… But if you’re looking for a great day to come to the 5th floor of Maloney, I’d recommend coming on a Wednesday.

Wednesday Tea, 4-5 p.m.

Thursdays may have seminars, but Wednesdays have tea.  That’s probably reason enough.  Above are BC math folk in their natural habit.  (Not pictured are people playing Go… we’re trying to get the game to catch on, but first we need to get more people that actually know how to play….)

Putnam Problem Solving Group, 5:30-6:30 p.m.

And after tea you can meander over to 560 to find the Putnam group stare at very hard (unnecessarily hard?) math problems.  Currently, we’re working through the 2015 Putnam exam.  Today we got through the first 4 problems… updates to follow.  The #5 and #6 problems are coming up next, and these problems aren’t getting any easier….

Anyway, as you can tell, Wednesday afternoons are mathtastic in Maloney.  As a matter of fact, sometimes I even have to remind myself not to have too much fun…

Kickoff Party 2016!

Today marked the beginning of a new year for the BCMS!

In case you missed it, we talked about the upcoming events for the year, Dawei gave an awesome presentation on flat surfaces, and we had a lot of pizza (nobody seemed to know what type one of the pizzas was… maybe eggplant, but we’re not entirely sure).

Some Upcoming Events for the Year:

Department Tea

• Time: Wednesdays 4-5
• Place: Maloney faculty lounge
• Who: Anybody and everybody.

Introduction to $\LaTeX$

• Time: September 21st at 5:30 pm
• Place: Maloney 560
• Who: Anybody new to LaTeX (i.e. are you in Intro to Abstract?) or anyone who wants to brush up on their typesetting skills

Career Panel

• Time: October 13th at 5:30pm
• Place: Higgins 310
• Who: Anybody who wants to learn what math majors can do after college

Piersquared Tutoring

• Details TBD
• Talk to Chris Ratigan

Putnam Problem Solving Group

• Time: Wednesdays (to be confirmed)
• Place: Maloney 560
• Who: People who like fun, math, and fun math

Movie Night

• Time: later in the semester
• Movie suggestions welcome

Problems That Were On The Board Today:

1.  You pick up a meter stick with 100 ants on it. Each ant walks 1 cm/s toward an end of the stick, and it reverses direction any time it encounters another ant. What’s the longest amount of time you’d have to wait for all ants to fall off of the end of the stick?

2.  Start from a place on the earth’s surface, travel south for 100 miles, east for 100 miles, and finally north for 100 miles and you get back to your starting point. Where did you start?

3.  How do you apply $+, -, \cdot, /, (, )$ to {3, 3, 8, 8} to get 24? Each number can only be used once (for example with {2, 2, 8, 8} we have (2 + 2) * 8 – 8 = 24).

4.  For what n, is n! equal to the number of seconds in 6 weeks?

5.  Let f be a real-valued function on the plane such that for every square ABCD in the plane, $f(A)+ f(B)+ f(C)+ f(D) = 0$.  Does it follow that $f(P) = 0$ for all points P in the plane?

6.  Show that there exists a convex hexagon in the plane such that: (1) all its interior angles are equal and (2) its sides are 1,2,3,4,5,6 in some order

7.  Show that every even integer greater than 2 can be expressed as the sum of two primes (again, if you solve this question, make sure to let me know so we can write a paper together)

Math is Everywhere

Almost everyone learns growing up that a line is 1 dimensional, a plane is 2 dimensional, and the space we live in is 3 dimensional. One day, a crazy theoretical physicist came along and argued that the universe consists of 4-dimensional space/time. That physicist’s name was Albert Einstein. A slightly less well-known name is Benoit Mandelbroit. Mandelbroit was a mathematician who argued something much more profound: dimensions are not discrete. The standard example of this phenomenon involves measuring the coastline of Britain. A Euclidean scientist would think that measuring Britain’s coastline with a smaller, more refined, ruler would give a more accurate measurement than a larger, less refined ruler would, and that with a small enough ruler, the length of Britain’s coastline could be determined to any degree of precision. This is actually not the case!

In fact, if the coastline of Great Britain is measured in units of 100 km, then its coast is roughly 2800 miles long. However, if our Euclidean scientist tries to refine this measurement by using units of 50 km, then the coast is 3,400 km long. That’s an increase of 600 km!

The reason for this apparent paradox is that unlike a boring line which has no new structure as you zoom in, Britain’s coastline has detailed structure on all levels of magnification. This new structure makes Britain’s coastline a naturally occurring fractal.

A true fractal is an object which is self-similar, meaning that as you zoom in on the fractal, you see smaller copies of it.

Examples of fractals abound. Three particularly interesting ones are: Pre-modern cities, the cells that make up the human body, and the stock market.

In pre-modern cities, particular cities which grew “naturally” out of collections of settlements, each group of people living in the city would want to have everything they need close to themselves. This

The fact that the cells that make up the human body are fractals is being used in cancer research. Any biology student would understand that the surfaces of cancer cells display different proteins than the surfaces of regular cells. Recent research has shown that cancer cells have a different fractal dimension than regular cells. This can be used to help better identify cancer cells and better design drugs targeted to the specific structure of the cancer cells.

The stock market is a very interesting example of a fractal because unlike the other two examples where fractals were used to find structure in pre-modern cities and normal cells, the fractal nature of the stock market means uncertainty. Fractals are not smooth, they jump around a lot on small distances. According to Nassim Taleb, this can be used for a different investment strategy. Instead of trying to predict which stocks will do well based on their history on the market, Taleb proposes investing small amounts in many different high-risk stocks. You will loose some money here and there, but all you need is one fractal spike on the market and you could make millions!

Believe it or not, your resting heartbeat is also a fractal and over time will naturally get to around 120 bpm without your noticing.