Last Lecture Semester II 2017

Arun Ram
Department of Mathematics and Statistics
University of Melbourne
Parkville, VIC 3010 Australia
aram@unimelb.edu.au

Persi Diaconis

Persi Diaconis is a famous and inspiring scientist, has been a great influence and mentor, and most important of all to me, a wonderful friend for more than 20 years.

A bio of Persi Diaconis

My story of meeting Persi

I had just finished my PhD in mathematics and was starting a Postdoc in Boston. I had heard that Persi was "friendly" to algebraic combinatorics (the general part of mathematics that my PhD thesis was in) so I went up to Harvard, where he was a Professor at the time, to meet him. His door was open, he was sitting at the desk. I introduced myself, gave him a little background about myself ("I'm a postdoc, just finished my degree last year, I did my degree in San Diego, I was a joint student of Adriano Garsia and Hans Wenzl. I've heard that you are also friendly to algebraic combinatorics, and so I thought I'd come up and meet you.") He asked me what I did (which, in the math world, means "What research did you do in your thesis?"). I told him I had worked on characters of Brauer algebras and told him briefly what a Brauer algebra was (I explained how it is a Schur-Weyl duality analogous to that between GLn and the symmetric group, except that GLn is replaced by On and the symmetric group turns into the Brauer algebra. I probably drew a few Brauer diagrams for him.)

d1= andd2=

At that point Persi asked "What do you want to know characters of the Brauer algebra for?" I was not so secure at that stage of my career (or even now), and I sheepishly said I didn't know, "I needed a PhD thesis and it seemed as good a problem as any other for me", and I thanked him, and excused myself rather rapidly.

After that I had no further contact with Persi. I went on to another postdoc at University of Wisconsin--Madison. It was about a year later ... the phone rang. I answered it, and the voice on the other end said "This is Persi Diaconis". I almost dropped the phone. I couldn't hardly concentrate at all, but I tried to remain focused, and he explained to me that he wanted to know a certain very specific character of the Brauer algebra. I made sure I understood exactly which character he wanted to know, and then I told him that I couldn't tell him on the spot, but that I thought I could work it out. He was very nice about it and gave me his number to call him if I got it worked out.

I worked solid on it for 3 days. I was nursing a head cold, so I would sleep a few hours, eat a bit, work on it for 5 or 6 hours, in a very strange cycle that didn't follow day or night.

3 days later I called Persi back and told him the answer for the character that he wanted. He very carefully went through it over the phone to make sure he got it copied down correctly. Then he thanked me, and I asked him "What do you want to know this character of the Brauer algebra for?"

I was not prepared for the answer. "Well, I'm doing some consulting for AT&T (the largest phone and communications company in the US at the time) and we're working on making encoder-decoder boxes so that on one end the signal can go in, get encoded and compressed to be more efficient for transmission, and then on the other end the signal gets decoded. It has to all be done in real time, because these are usually voice or fax transmissions. So had this idea that we could use random orthogonal matrices and in working out the calculatios for it we seem to need this character of the Brauer algebra and so I thought I'd call you. I think we'll be writing a little paper on this algorithm, I'll send it to you when its ready."

And, sure enough, a couple of weeks later, a research paper from Persi arrived in the mail at the Math department for me, with a nice couple of lines thanking me for computing this character of the Brauer algebra for them.

I learned an important lesson: about how others may need my results and could benefit from my work in ways that I was unable to think of. Lots of time they don't even know that they need my results (and I don't know that they need my results). Thankfully we have people like Persi, who have this miraculous ability to be able to connect problems and people and put together knowledge from different places to good outcomes.

I also found out that people in the communications industry were keen to give me a job. But, it wasn't quite my ideal, that wasn't really the idea I had in my head when I signed up to do a PhD in mathematics. But it was nice to know that I wouldn't be unemployed if it somehow didn't quite work out the way that I had in mind.

Gauss in kindergarten

The story goes, that one day in 1782 when Gauss was in kindergarten the teacher was in a very bad mood. He'd had a fight with his wife or something that morning, things just weren't going right that day and the last thing he wanted to do was deal with a bunch of 5 year old twirps. So he came in, put his books on the desk and told them to add the numbers from 1 to 100, and if he heard one word or peep from anyone before it was complete he would send them to the headmaster for a beating.

Gauss was calmly looking out the window at the cows in the field next to the school. He didn't feel like adding up the numbers from 1 to 100.

After a few minutes, the teacher noticed Gauss not working and became angry and asked Gauss why he wasn't working. Gauss said he was finished. The teacher told him to bring his slate up front and prepare himself for a trip to the headmaster.

Gauss brought his slate up. On it was, 10100, and then 5050 with a box around it. The teacher, of course had no idea if it was correct: 1+2+3+ ... +99+100 ?=? 5050.

How did he do it? My wife (a violinist by profession who went to conservatory for musical training and not to University) likes this example because it shows the beauty and power of mathematical tools.

1 2 3 4 5 98 99 100                   100 99 98 97 96 3 2 1                   101 101 101 101 101 101 101 101
10100
5050

Helpful skills for Maths and Science

ASK ME A QUESTION

LISTENING

SPEAKING

ORGANISATION

LANGUAGES

READING MINDS

Key advantages of being in Maths and Science

PEOPLE THINK YOU ARE SMART

You know they're wrong, but it doesn't hurt that they think so.

PEOPLE THINK THAT BECAUSE YOU'RE SMART YOU CAN DO ANYTHING

You know that they are wrong, but that you CAN LEARN to, when you want to.

PEOPLE THINK THAT BECAUSE YOU CAN DO ANYTHING THEY SHOULD GIVE YOU A JOB

You know that you're not really qualified, but that YOU LEARN fast, and you'll probably do just as well as anyone else that they could hire.

THE DOOR IS AJAR, ALL YOU HAVE TO DO IS OPEN IT

The secret is, ... push, ... but don't push too hard all at once or you'll break the hinges and fall flat on your face when it falls in, ... so push just a bit firmly, and don't give up. The door doesn't open right away, but it will if you keep focused and keep working on it.

GOING UP!

Education

My father was an academic through and through. He was proud of being an academic and proud of what he had been able to achieve with an academic career.

I was the eldest son of the eldest son from an orthodox Hindu family. In that culture that means a lot. A lot of advantages — and a lot of responsibilities. There was an assumption that I would follow my father’s steps and become a theoretical physicist. Of course, my father had already seriously accelerated the process of breaking the traditions by marrying my mother, an American from Colorado. Quite far from the arranged marriage to the daughter from a good family that was the norm in his tradition. Nonetheless, I presented my father a great emotional challenge. I did not become a physicist. I became a pure mathematician. In my father's eyes he could see that he had obviously failed to raise his son properly.

My brother Nilam was 5 years younger than I and would have none of it. “I’m not going to be an academic like you guys. I’m not going to be poor all my life!” By this time my father gave the impression that he had mostly given up and my brother had looser reins. Also, my brother was the second son, so he was a bit more free, and had bit less of the wonderful special treatment than I had had. But my brother turned out ok in the end. This is the story of my brother’s education.

My brother graduated High School in New Mexico and went to New York City to do his undergraduate degree at Columbia University. He majored in international finance, and did an internship at the Swiss bank, Bank Juilius Baer, in his last year of college. When he finished his Bachelor’s degree at Columbia University the bank offered him a job as a junior trader in foreign currency. My father was relieved that my brother was employed and not starving.

Six months later my brother received his first Christmas bonus at the bank. I had finished my PhD in pure mathematics two years before and had a reasonably prestigious postdoctoral position at University of Wisconsin. My brother’s Christmas bonus after 6 months of trading foreign currency was equal to my annual salary. My brother was very proud, and rightly so. He had one upped his elder brother in a truly substantive way. I talked to him on the phone and congratulated him. I could hear the pride in his voice. Well deserved.

I talked to my father that weekend. He hadn’t heard the news yet and so I told him that Nilam had received a Christmas bonus at the bank which was equal to my yearly salary. My father responded, in his heavy Indian accent:

Very Goodh. I have vun son hoo is succcesssful, …. and vun son hoo is richh.

My brother is intense and efficient and a very hard worker. He traded with focus. When I would visit him in NY, he would get up in the middle of the night when Tokyo opened, make a few phone calls and go back to bed. Maybe the same for London, and then he would be up early to be on top of it for New York opening. After a breakfast of bagels and coffee together, my brother would have a long day at work at the office, then dinner with me, and then more phone calls to overseas clients during the night. It wasn’t very long before my brother wasn’t junior trader anymore. He was managing a pretty serious portfolio.

Five years later I was talking to my brother on the phone.
He said, “I quit my job”.
I said “WHAT? Why? Everything all right?”
He said: “Yeah, everything’s fine, I was getting a little bored with this routine, and I’ve been thinking, and so I went into the president of the bank and asked him when he thought I might be president of this bank?”
I said: “YOU DID WHAT?”
He said: “Yeah I asked the president when I might become president of the bank.”
I was in shock.

I said: “What did he say?”
My brother said: “Yeah, actually, he was pretty cool about it. He said that he figured that I was actually pretty talented and that probably in 10 years I would be president of the bank. I told him that’s too long. So I quit and cleared out my desk and said goodbye to my team and left the bank.”
There it was. My bother had quit the bank.

I asked my brother: “So what are you planning to do?”
He said: “I don’t know yet really. First, I think me and my girlfriend are going to take a trip to Thailand for a month or two. Then, maybe I might go to graduate school.”
I asked: “What field are you thinking?”
He said: “I'm thinking maybe psychology, that’s what I find really interesting, dynamics between people in the office, psychology of relationships with my clients, dynamics and interactions of people on the street.”
I said it sounded reasonable.

After all, what could I say? -- the guy wasn’t a poor academic like I was. He could certainly afford take himself to Thailand and then put himself through graduate school if that is what he wanted to do.

The next day I was talking to my father on the phone.
Me: “Did you hear Nilam quit his job?”
My father: “Qviit hees joub? Vaat doo U meein?
Me: “I mean, he quit his job. He’s not working at the bank anymore.”
My father: “Vaat is hee goooing to doo?”
Me: “He said he’s going to take a holiday and then he’s thinking he might go to graduate school and get a PhD”
My Father:

“That’s veery gooood. The boy is faainally goooing to gettt an educayshunnn.

Semester 2 discovery: David Foster Wallace

David Foster Wallace on Roger Federer

YouTube Radio Thursday night at home

Juan Bernal

I found this link this morning, I need to copy the text here

Thank you.

Arun Ram
Department of Mathematics and Statistics
University of Melbourne
Parkville, VIC 3010 Australia
aram@unimelb.edu.au

This was the sketch for thelast lecture of MAST20009 Vector Calculus and MAST30026 Metric and Hilbert Spaces in October 2017.