coxeter groups
san francisco state university
universidad de los andes
federico ardila
2008



. forum . homework . lectures . people . projects . syllabus . texts .



at the request of several of you,
these are the people at the other end of the camera.

"berkeley" is math.berkeley.edu, "gmail" is gmail.com, "sfsu" is sfsu.edu, "uniandes" is uniandes.edu.co, "en" is @, "dot" is .




. aaron . addie . alex . amanda . andrea . andrés . andrew . benjamín . brandon . carlos . carolina . césar . cristian . danilo . david b . davidr . eric . federico . felipe . gustavo . henry . iván . jack . jameson . jeff . jon . josé . juan camilo . katrina . kristen . laura . luis . mariana . mike . mitchell . thomas . vladimir .



aaron dall . adall en sfsu

I sing my songs in this tended garden.
I play in parks with Neruda often.
I do practice yoga. I do sit zazen.
I play with mathematics every now and (every) then.

In particular, I am interested in modular flows on graphs, face rings of simplicial complexes, monomial ideals, and toric varieties.

In general, I am interested.

addie evans . adde en sfsu

This is a picture of me after I just gave the final for my Math 59 class last semester. I really love getting paid to bang on about math and entertain students with my dorky giddiness over basic Algebra. I'm working towards my Master's degree in Math and am mainly interested in Applications and Statistics, specifically for Ecology. However, of all the Pure Math, Combinatorics seems the most fascinating to me. Of the many intellectual ambitions I once had, I have distilled them down to the three most important: getting a PhD., writing a book and trying to become fluent in Spanish. I also love dance and I am currently studying ballet and modern jazz, but I have studied modern, west african, afro-cuban, swing, and salsa (+merengue, cha-cha-cha and bachata). My other interests are knitting, aromatherapy, surfing, yoga and feminism.

alex fink . finka en berkeley

Sightings of Alex Fink reported over the last one and a half years have clustered around Berkeley, California, particularly in the vicinity of Evans Hall. The species apparently displays migratory tendencies: it's been known (bizarrely) to spend parts of the winter near its (far chillier) fledging grounds in Calgary, Alberta. Easily recognisable by the broad drooping flaxen plumage on the back of the head.
I've just taken up with Bernd Sturmfels as my intended PhD thesis supervisor. Plans, as of yet essentially uncommenced, are to work on some topic near the meeting of tropical geometry and matroid theory. That said, my mathematical interests are fairly diverse, including very many topics of algebraic or discrete nature, and bleeding into computer science. Outside of mathematics (there's an outside?) I'm into constructing languages, and am part of a team composing the Second Google Puzzle Hunt.
This is my second time cross-registering in one of Federico's courses (and how can I resist: electrons cross the bay -- or Central America -- so we don't have to!). Last year I took matroids, and my final project with Felipe Rincón and Santiago Saavedra blossomed into a paper now on the arXiv. I look forward to another project with equal potential.

amanda ruiz . alruiz en sfsu

I wasn't 6 when I realized I loved math, I was 23. I was working in an education non-profit in Oakland and I heard a song. The name of this song is "Mathematics". Its by Mos Def. He says. . . " Young bloods can't spell but they can rock you in PlayStation this new math it whippin m&8%er@*^#ers ass you wanna know how to rhyme you better learn how to add It's mathematics". (Read all the lyrics.) Its a great song, you too should love it, too. Anyway, 5 years was enough to get over the trauma of my secondary education in Huntington Beach, CA, and I allowed myself to embrace mathematics, previously only known to me as a subject you have to put up with in high school. I left Orange County (also known as the orange curtain, for its repressive and conservative culture) to go to college at UC Berkeley (the best school ever) and in rebellion to all things that could be considered high school subjects, I created my own major, called "social change and social control." This led me to my first job as a college graduate, which I mentioned already. Then that led to teaching high school math, which led to burning out and wanting nothing more than to go back to the good ol' days of being a student. So I went back to school. My goal, to get a 2nd bachelors degree in Math, led to my goal of getting a Masters degree in math, which, naturally leads to my desire to get a PhD in math. I've completed a year of my Master's program, and in just one short year went from drawing 5D cubes for fun to becoming a math talk junkie, I go to just about every math talk I can find. My project from Matroid Theory last year has turned into a nice little paper, and according to my horoscope (which i believe in because it is convenient for me to this year) I have a lot to look forward to in the next 12 months, including getting published, traveling the world, and making lots of money! (2 out of 3 wouldn't be bad)

andrea rincón . ap.rincon150 en uniandes

I was born in Bogota. I live in Bogota an study math at Los Andes. I like to paint, listen Music like Jazz and Rock ... I also like to read Manga and watch Anime. I woul like to work in somethig like Matroids and Topology or Knots, i also like Mader matroids.

andrés lizcano . a.lizcano51 en uniandes

I was born in Cali, Colombia in 1988. 1990 I went to Germany, where I lived in a town near Karlsruhe for almost 8 years. 1998 I returned to Colombia. I finished highschool in Bogotá and now I'm coursing 4th semester of mathematics. My main mathematical interest is to learn and find out how to solve problems the best way. Any kind of problems. I like modern algebra and lately I'm starting to feel interested in finances. But i hope to learn more about my own mathematical interests. I also like climbing and traveling and learning about Colombia and other countries!

benjamín iriarte . b-iriart en uniandes

Four years ago, when I was at school, it would have never ocurred to me that I was going to study math, what I cared most about was music, composition. But I had this sort of longing, I remembered how really fun and rewarding it was to solve math olympiad's problems (which I did when I was younger) and that actually I was good at the stuff, so I really started feeling I had missed something important (or even fundamental) about me by not caring about it at all. So here I am, happier than ever, studying the BS in math at los Andes, it was probably the best decision I took ever. What I enjoy the most is number theory and combinatorics and I'm interested in open problems in those areas, so I'll probably look for something related for the final project.

andrew herrmann . aherrman en sfsu

brandon stickel . iamasquare en gmail

greatest things in life:
discovering beauty, seeking knowledge, playing jazz, libraries, climbing to the top of a mountain, sunshine, rilke's poetry, cooking, the excitement upon opening a math text and looking at unfamiliar symbols and not understanding anything and wondering what it all means and knowing that with patience i can understand.

carlos rodríguez . carlo-ro en uniandes

I was born in Bogotá, a lovely, some times cold, but always interesting city, where I've spent my entire life (23 years) until now. When I'm no studying I like to spent my time with my friends, I also like riding, and I have a special interest in electronics and image processing. Two things which I want to learn (as much as I can, and as sooner as possible), are photography and music.

carolina benedetti . c.benedetti92 en uniandes

I was born in Bogotá 23 years ago and last year I've begun the master at Los Andes... About things I like are sushi (I love seafood), and I enjoy cooking too (someday I have to do it more serious). When I'm not studying I'm playing some game (board games) or practicing some sport, mainly volleyball... or I'm simply playing with my nephews or in the cinema or hearing music like funk, progressive rock and others...

césar ceballos . ca.ceballos954 en uniandes

I was born in Cali,Colombia. I'm 20. Last year I finished my undergraduate in mathematics at Universidad del Valle (in Cali) and this year I began the master's program at Los Andes. I get very excited doing maths and dancing salsa music (most with maths)....ah! with women too. My classmates said I'm the most flirt of the master's program. (I think they're wrong.)

cristian martínez . cm.martinez en uniandes

I was born in Cali-Colombia "the flavorland" 23 years ago. I studied my undergraduate in the Universidad del Valle (Cali), where my interests was centering in Algebraic Topology. After finish my undergraduate, I moved to Bogotá to study the master in the Universidad de los Andes, where I worked in Algebraic Geometry and Algebraic Topology again. This year I began my PhD in the Universidad de los Andes.
My interests: Maths, women and beers.

danilo pardo . jos-pard en uniandes

My name is Danilo, I am 23 years old, colombian 100%. I studied 1 year in italy, came back and startet studying mathematics, 5 years ago. I had to stop more than 1 year, then I went to new jersey, where i worked for 8 months, so I am still missing some subjects. I like algebra, and topology... and sports, basketball and soccer. I have a twin brother, I love it, i like dancing, parting and having fun.

david bangor . dbangor en sfsu

I was born in Santa Monica California and soon moved up to the eastern mountains of San Diego to a small area known as Ramona. I kept myself busy skateboarding and during my last year of high school I came to really enjoy mathematics. I did my undergraduate work at San Diego State University majoring in applied math with an emphasis in physics. This is my second year at SFSU in the masters program. My interests in mathematics has turned to topology and analysis but recently I have been interested in algebraic structures and their representations. I spend most of my time riding my bicycle all over the bay area and touring as much as possible. I have really enjoyed my time up in San Francisco and I am looking forward to what the future will hold.
Always be cautions of cyclist and celebrate the beauty self propelled transportation.

david rincón . dav-rinc en uniandes

I was born in Bogotá, Colombia. I'm 19 years old and currently on 5th semester of mathematics. I still haven't had much experience with the different areas of mathematics, but definitely logic and algebra are, and will be my favorites.

federico ardila . federico en sfsu

I was born and grew up in Bogotá, Colombia. I spent 9 great years studying mathematics at MIT and braving the extreme Boston winters and summers. (Even a Colombian has heard of "fall" and "spring" - why haven't they?) After three amazing years in Bogotá, Berkeley, and Seattle, I have been in San Francisco since 2006. I am now an assistant professor at San Francisco State University and an adjunct professor at the Universidad de Los Andes in Bogotá. My main mathematical interest is to study objects in algebra, geometry, topology, and phylogenetics by understanding their combinatorial structure. I have several projects that I would like your help with!
When I am not at work, you might find me on a fútbol field, treasure hunting in little music stores, or exploring the incredible cities of San Francisco and Bogotá with my wife May-Li.

felipe rincón . feliper84 en gmail

I was born in Bogotá, Colombia. I have liked science, specially mathematics, since I was a child. I participated in some math olympiads when I was in highschool, and that's how my love for this art started to grow. I studied math at the Universidad de los Andes for 6 years, and I'm right now starting my math studies at Berkeley. During this time I have become interested in several areas such as algebra, topology, combinatorics, logic, and set theory.

gustavo ruiz . gu-ruiz en uniandes

My name is Gustavo Ruiz. I was born in Bogota, Colombia in 1985. Actually I'm working in Seguros Bolivar, I'm an Actuary adviser. I am interested in applied mathematics, I am planning to do a master in actuay. In my free time I play soccer it's my favorite sport.

henry león . ha.leon50 en uniandes

my name is Henry León I'm a mathematician from the Universidad Nacional de Colombia, at present I'm in the first semester of the Master of mathematics in Los Andes. I like the topology and I wait to work in differential topology across the master.

iván contreras . iva-cont en uniandes

I'm 22 and I was born in Bogotá, Colombia. Since I was 14, I discovered that I liked mathematics and I began to participate in math competitions. In fact, in this moment I'm working on the National Olympiads Organization in Colombia. I'm in my last semester of mathematics in los Andes and I hope to be admitted in a master program abroad (I applied to SFSU!!!!).
My area of interest includes Differential Geometry and Algebraic Topology. When I'm not studying I play  fútbol (official goalkeeper of my team), jog in the morning and watch TV...

jack abad . jackabad en sbcglobal dot net

I was born in San Francisco in 1934 and graduated in mathematics from the University of San Francisco in 1956. I spent my career in the San Francisco Unified School District as a mathematics teacher, principal (Galileo High School), and central office administrator (Director of Personnel, Employee Contract Negotiator) until my retirement in 1993. After my retirement, I taught part-time at the University of San Francisco for a few years I have taken for credit or audited a number of courses at San Francisco State in mathematics: number theory, algebraic curves, matroid theory, and combinatorics. My main interest in mathematics is in discrete mathematics. I subscribe to the MAA journals and, in collaboration with my two brothers, who are also trained in mathematics, submit solutions to problems published in their problem sections.
Mathematics is my main interest outside of my family I have four children, two from my first marriage aged 46 and 49, and two from my second marriage, 25 and 30. I also enjoy babysitting my three-year-old grandson, watching Warrior games, going to movies, and reading.

jameson cahill . meson en sfsu

I was born and raised in Anchorage, Alaska, but I have lived in California for about ten years now. I have been at San Francisco State for four years now, I received my BS one year ago, and plan to finish my MA one year from now. I have been working in the field of functional analysis for the last several years, and have recently been making some good progress (finally). I never knew about matroids before this class, but I find the subject quite captivating. When I am not doing math I like to make electronic music, and maybe someday I'll start playing an instrument again.

jeff doker . doker en berkeley

Things I take: Pictures, found money, criticism, risks, you seriously, bike paths, one for the team, the road less traveled, it to the limit.
Things I make: New math, new songs, fun of myself, long Frisbee throws, poignant observations, food disappear.
Things I shake: Pulpy orange juice, maracas, the bag of Scrabble tiles, what my mother gave me, it up.

jon yaggie . jyaggie en sfsu

I was born in Michigan; however, I have lived in several places over the past ten years including Greece, Russia, and most recently San Francisco. For fun, I enjoy gathering mushrooms, learning languages, reading, and sleeping. I have a seven year old son, Sebastian. Academically, I am interested in algebra and geometry. I am hoping to extend my limited knowledge of combinatorics in this class. I should graduate with my BA this semester!

josé samper . ja.samper914 en uniandes

I was born here in Bogotá in 1988 and i have always lived here. To spend my free time i like to play the guitar and i'm learning to play bridge. I'm interested in number theory and combinatorics.

juan camilo salazar . juan-sal en sfsu

I was born in Bogota, Colombia. I loved math since forever. I'm also interested in computer science, I'm currently doing 2 careers: mathematics and systems engineering.
I'm interested in algebra, geometry, number theory and computational mathematics.
I like anime, manga, occasional kakuro and sudoku games.
I love traveling, I've been to the U.S. (great trip to Las Vegas, Seattle, Californian coast, etc.), Chile, Argentina, Ecuador, Venezuela, Peru, France, Italy, Greece, Spain, Monaco, Vatican City and United Arab Emirates.

katrina wono . katrinawono en gmail

I was born and grew up in Jakarta, Indonesia. and I came to the US almost 10 years ago. I have always loved math for as long as I can remember, and yet, I chose Electrical Engineering as a major in college. Two years into the program, I knew that it was not the right major for me, unfortunately, changing major was out of the question back then, back there. It took five and a half years until I finally got my bachelor's degree. That was 1995. In 2005, I decided to go back to school, and I ended up repeating all of the lower division math at DVC, and after that, I felt like I wanted to continue taking math classes. So, last semester, I started taking upper division math classes through the Open University at SF state. I would like to apply to master's program, but I just haven't quite decided when.

kristen freeman . kdfreema en sfsu

I was born in the bay area and have lived more or less in Northern California all of my life. I'm in my second semester as a graduate student and love every minute of it. I tend to overwork myself and am compulsively organized; I have all paydays, due dates, and holidays noted in a calendar I keep at the ready. I enjoy music of all kinds - classical to rock to world - and while I don't play very much now I still like to spend some time with a piano or mallet instruments since first studying music at age 6. On top of schoolwork I'm also currently working on a research project with Federico about Tropical Oriented Matroids and teaching two remedial algebra courses. I have no specific interests for our final project - I particularly enjoy Linear Algebra and Combinatorics, but there are just too many choices - so I'm open to different ideas and working with someone from Bogotá; beware though, my four years of high school Spanish are steadily slipping away from me.

laura escobar . la-escob en uniandes

My name is Laura Escobar. I was born in Medellín, Colombia, but I grew up in Bogotá. I'm studying mathematics at Universidad de los Andes, and I'm currently on my last semester. So far I have liked algebra, topology, logics and set theory. I don't know a lot about combinatorics , but I'm really interested in it. I like learning about different cultures in the world. Because of that I like to learn languages and travel. I'm currently studying japanese and I would love to go there.

luis garcía . alb-garc en uniandes

I was born and raised in Bogotá, Colombia. I'm 21 and currently in my last year of my undergraduate math studies here at los andes. I was an econ major first, but I found that math was more fun and interesting. The way I discover new things in life is like a juggling act: i tend to be interested in many things and try to handle them all at the same time, sometimes I drop them because I get bored or simply can't go on... the good thing is I can always start over again. Some random stuff I've been doing/ thinking/amazed by: art in all its forms, contemplation of life, life itself, astronomy, literature, word puzzles, movies, good humour, comic strips, zen buddhism, and math, of course.

mariana laverde . mar-lave en uniandes

I was born in Bogotá, Colombia in 1986. Nowadays I'm studying Math at Universidad de los Andes. I have always lived in Colombia. From the things I've study in mathematics I like algebra, geometry and combinatorics.

mike jackanich . mikejack en sfsu

I was born in San Franciso and lived in the area most of my life. I am currently in my second year of the masters program at SFSU. I previously received my undergrad degree (in math) from a small school in West Virginia. The school was call West Virginia Wesleyan and my main reason for going there was to play baseball for the school. My math interests are geometry and algebra. Now a days when I'm not doing math, I enjoy coaching baseball at a high school in SF and playing for the best intermural soccer team that SFSU has ever seen.

mitchell oster . oster en sfsu

Hello all. My name is Mitchell. I was born in Tijuana, B.C., Mexico 37 years ago and grew up in San Diego. I've lived in SF for 13 years. Married, no children. I love baseball, politics and my sobrinos (that's nieces and nephews for non-Spanish speakers). I'll be graduating this spring semester and am applying to the Master's program here at SFSU for this fall. My goal is to teach at the Junior College level. I love Algebra.

thomas rizzolo . trizzolo en sfsu

I grew up in New York City where I received my Bachelor's degree in Mathematics with a minor in Computer Science. After I graduated, I took some time off to pursue another strong interest of mine. I went to Beijing, China to learn Mandarin Chinese and ended up staying there for a couple of years. Now that I am back in America, I decided to start my Master's degree at San Francisco State University. My Math interests include: Geometry, Set Theory, Logic, and Math History (specifically Asian Math History).

vladimir durán . vladimir en sfsu

I'm the son of two El Salvadoran immigrants who met in Brooklyn, New York where I was born. I lived in New York until I was 13. From there I moved to Los Angeles, California where I went to high school (San Fernando HS ) and community college (Santa Monica College). After that I transfered to UC Berkeley where I obtained my BA in Mathematics. I'm now finishing my Masters at SFSU. I'm writing my thesis on how Composition Operators behave on a particular Banach Space of Analytic functions defined on the unit disk in the complex plain. My main mathematical interest comes from Complex and Real Analysis. I find complex function theory to be very beautiful and elegant and I encourage anyone to dig deeper into this subject. Other mathematical interests include but are not limited to Algebraic Topology and Differential Geometry. Hatcher's Algebraic Topology is great resource to start learning this subject. Spivak's Differential Geometry is on my current reading list. I'm getting through the 2'nd volume. Non mathematical interests include reading novels: Garcia Marquez 100 years of Solitude is my personal favorite, with a close second Vonnegut's Sirens of Titan. Also playing electric bass is one my favorite hobbies. Looking forward to working with old friends and making new ones.