Spotlight: Elizabeth Pacheco, Department of Mathematics, OU.

We continue our Spotlight series where we highlight one of the member of the OU Math Department. This edition of Spotlight shines a light on one of our most accomplished graduate students, Elizabeth Pacheco


Short bio (in her own words): Elizabeth is a fifth year graduate student in the math department at OU. She has a B.S. in Mathematics from the University of North Texas. She is studying (configuration spaces and Leavitt path algebras) under the guidance of Dr. Murad Ozaydin.

The blog caught up with Elizabeth to get her thoughts on mathematics, graduate study, cats and other important topics.

1. What made you decide to pursue mathematics?
I realized that the answers at the end of any math problem were far more satisfying to me than any other subject. Also, math was (and is) pretty fun – I’ve always enjoyed puzzles.
2. What are some of the rewarding things about being a mathematician?
I like how humbling mathematics is. I’ll never know all there is to know, which is both depressing and freeing.
3. What are your other interests besides mathematics? Favorite band? Snickers or M&Ms?
I like games – card games, computer games, board games. I also enjoy teasing my very grumpy cat, Schrődey. My favorite band – Queen. And definitely M&Ms – I’m allergic to peanuts.
4. Who is your favorite mathematician and why?
Although, he’s pretty popular, I have to go with Erdős. I like the problems he would come up with and/or popularize. He strikes me as a bit of a math rock star, and I like his belief in “the book.”
5. Discuss some of the challenges students face in graduate school and your suggestions to overcome them.
The struggles I notice as are feeling as if you know noting and the difficulty of learning new things. I’m still in the midst of overcoming some of them. What has helped me somewhat is taking to professors or fellow graduate students – it helps you gain clarity when you are discussing your confusions, or solidify your understanding if you are teaching a concept.
You should also attend talks – it’s sometimes surprising to realize how much you have learned by attending talks, even if you don’t understand everything of what is said.
Also, for me, playing with my cat is a big stress relief. No matter how you slice it, you are never alone in this.
6. Describe “a day in the life of a mathematician” as it applies to you.
My schedule is rather fluid, but the morning and afternoon are usually spent on classes – both those I teach and attend, and the evening is spent on reading and trying to understand papers.
7. Tell us, if possible, a little of what is your research area and what you are currently working on.
Dr. Özaydin and I used to talk about configuration spaces a lot, but right now we are discussing Leavitt path algebras. A brief explanation of this would be: take a graph, and consider the algebra of paths on this graph (elements are formal linear combinations of paths with coefficients on some field and these elements interact under addition and concatenation of paths, where two non-incident paths concatenate to be zero). You can ask questions about properties of the algebra you just created and/or you can use the construction to provide examples of rings with interesting properties, such as rings of a given basis type.

Spotlight: A chat with Dr. Keri Kornelson

In this new and hopefully recurring feature we hope to introduce you to some of the faculty members in our department. We recently caught up with the busy yet always available Dr. Kornelson.

Keri Kornelson

Brief Bio: Dr. Keri Kornelson is an Associate Professor in the Department of Mathematics.  She received her PhD in 2001, specializing in abstract harmonic analysis.  She held a postdoctoral position at Texas A&M University and was an Assistant Professor at Grinnell College in Iowa before coming to OU in 2008.  Her research is in the areas of harmonic analysis, frame theory, and Fourier analysis on fractals.  Her work has been funded by the Woodrow Wilson Fellowship Foundation, the National Science Foundation, and the Simons Foundation. She is also interested in new teaching methods, active learning, and exploring the use of technology for instruction.  You never know what you’ll get in her courses these days!

We had the chance to ask her a few questions. So here is a peek into the professional life of one of the mathematicians at OU.

1. What made you decide to pursue mathematics? What led you to becoming a mathematics professor?

     Somewhere toward the end of my Junior year as a physics major, I realized that the physics wasn’t as captivating to me as the math.  I loved the underlying mathematics, but didn’t get as excited about the physics.  I changed my major to math right away.  I still liked the applications, though, so I took a job in the aerospace industry for a while before coming to graduate school.  Being a math professor is by far the best job I’ve ever had, though.

2. What are some of the rewarding things about being a mathematician?

There is a terrific balance to this job between creating/discovering/understanding new mathematical ideas and helping others discover mathematical concepts for themselves.  It’s a mix of feeling the wonder of complete confusion when doing research and being the instructor who shows others how to persist in the face of that confusion.  You never feel too smart, or too stupid, in this job.  It’s a wonderful place to be.  

3. What are your other interests besides mathematics? Favorite band? Snickers or M&Ms?

Interests:  Playing with my geriatric dogs, gardening, cooking, being outside when the weather permits, very amateur salsa dancing.   Band:  the subdudes  Candy:  Both, of course!  In the freezer.   

 4. Who is your favorite mathematician and why?
I know many would pick someone long past that everyone recognizes — Hilbert or Noether or Bernoulli or Gauss.  My favorite, though, is my advisor, Dr. Larry Baggett.  You should check out his book  In the Dark on the Sunny Side: A Memoir of an Out-of-Sight Mathematician.   His work in abstract harmonic analysis is elegant and precise.  He calls it the perfect blend of analysis, topology, and algebra.  More recently, he made his mark in the theory of wavelets and frames, introducing generalized multiresolution analyses.  He is just an amazing mathematician, person, and friend.  I wouldn’t be the mathematician I am today without his guidance and support.

5. Discuss some of the challenges students face in graduate school and your suggestions to overcome them.

The answers to almost every challenge in graduate school are a) find a network of fellow students to support you through the tough times and b) keep putting one foot in front of the other.  Everyone gets to a point when the mathematics gets really really hard, is coming very fast, and a big test or talk is looming.  No one is born knowing this stuff, everyone has to learn it.  You have to trust that time, hard thinking, working loads of problems, trying examples, drawing pictures, and discussing problems (math and otherwise) with your network will lead you to know more than you did before.  

Your path will be different from everyone else’s, by the way.  Don’t worry about that.  Just keep walking on your path.  

6. You have been very active in increasing participation of women and minorities in the STEM disciplines. What more should we do or what should we do more of? What is your advice to someone from an underrepresented group pursuing mathematics?
Oh boy, that’s a question.  If I had these answers, I’d get a grant and just fix it.  I don’t know the answers, though, so what we should do is keep thinking about it and trying stuff.  
My advice to all students, but especially to students who look around their science, engineering, or math classroom and don’t feel like they have had the same experiences as the others, is sort of the same as I gave to graduate students.  
Find a network/study group and work together.  Help each other learn the material, and quiz each other to be sure everyone’s got it.  It takes a little while to figure out good people to study with, so don’t be frustrated if your first attempt at forming a group isn’t perfect.
Keep putting one foot in front of the other.  Persistence is by far the biggest indicator of success.  Einstein’s claim about 5% inspiration and 95% perspiration absolutely holds true in your courses.  Do the homework, but also quiz yourself often, and mix up the problems.  That will deepen your learning.   
Maybe one more tip…use the resources.  Go to office hours, use the Math Center, ask questions in class even though it’s scary, look for videos online, work extra problems from the book.
7. Describe “a day in the life of a mathematician” as it applies to you.

My days vary a lot.  Some are mostly focused on teaching, getting ready to teach, making class activities and material, and meeting with students.  I try to do a little research most days, but some days are my true research days where that’s my main focus.  Then there are days where I help my colleagues on the projects that keep this awesome math department going and contribute to making it better and better.  

8. Tell us, if possible, a little of what is your research area and what you are currently working on.
My research is in harmonic analysis.  This often entails representing objects in terms of an agreed upon set of building blocks.  The blocks depend on the setting:  Fourier transforms use sine and cosine functions as building blocks; wavelets involve picking a fixed function and then doing shifts (translations) and stretch operations (dilations) to make all the building blocks.  I work on frames, which are sets of building blocks that have some redundancy, so you can build the same object in more than one way.  Like your friend loaning you some blocks from their set to combine with yours.
Once you pick a set of building blocks, you must figure out what to build.  Sampling theory involves a set of instructions with your blocks that tells you how many of various kinds of blocks to use, but not what you are building.  Thats what you have to figure out.   I’m working on a problem finding general solutions for certain kinds of samples right now.

Kudos Emily Scheele!!!

50ca3e9862e4f.preview-620Congratulations to one of our Math Majors: Emily Scheele was nominated for and has been awarded the Molly Shi Boren Volunteer award. This award, named after University of Oklahoma first lady Molly Shi Boren, recognizes OU students who have made a significant difference to the OU community by volunteering and making a difference. Please join the blog in congratulating and celebrating the stellar achievement of Emily Scheele.

Kudos!!! OU students at NCUWM

NCUWM: Nebraska Conference for Undergraduate Women in Mathematics

Every year, the University of Nebraska at Lincoln hosts a conference for undergraduate women in mathematics. The conference is open to all and women interested in mathematics are encouraged to attend and give talks on their research. This year the conference was held January 31st to February 2nd.

The OU Math Department send a contingent of our majors/minors to Nebraska every year accompanied by a faculty member; this year the following OU folks made it NCUWM:

Students: Jacquelyn Porter, Ashley Young, Laura Kincaide, Emily Scheele, Sarah Coulson, Terea Ratashak. They were accompanied by one of our graduate students, Tetyana Malysheva and a faculty member, Dr. Ralf Schmidt. Here are two pictures from their trip up North.

Trip to Nebraska by OU students

Trip to Nebraska by OU students


Trip to Nebraska by OU students


In a first for OU students, two of our undergraduate women presented at the conference. Sarah Coulson presented a poster titled, “Signature Authentication using Wavelet and Fourier Analysis” based on an REU she did at Texas A&M. Teresa Ratashak gave a well received 15 minute talk on, “Ranking Math Departments using the Google Page Rank Algorithm“, based on her undergraduate research project with our own Dr. Jon Kujawa.

Please join me in congratulating our students on a very successful trip!


Math Club talk: Friday, November 15th at 2:30 pm in PHSC 1105

This week we have an invited speaker in the Math Club, Dr. Liz Stanhope from Lewis & Clark College. Please join us for some intriguing mathematics and free pizza! Please note the unusual date and time.


Dr. Liz Stanhope.

Title of talk: “Orbigraphs:  Defining a graph theoretic analog to Riemannian orbifolds”

Abstract: A Riemannian orbifold is a topological space that is smooth enough to allow for calculus at all but a sparse set of singular points.  Much of my research has asked “Can you hear the singular set of an orbifold?”  That is, if you (in theory) set an orbifold resonating would the sound alone be enough to learn things about the geometry or topology of the orbifold?  In this talk I will discuss the efforts of my undergraduate research students to transfer this question into the setting of spectral graph theory.  I will try to convince you that this is a natural and interesting thing to do, and present some intriguing preliminary results.

“Why Are There Still So Few Women in Science?”

Recently there was a very interesting article in the New York Times Magazine entitled “Why Are There Still So Few Women in Science?”  You can read it here.

It is kind of long, but well worth reading.  It talks about the experiences of women both past and present in the science and why even now we end up with less women in these fields.  The very short answer is that even though lots of progress has been made, there are still a lot of ongoing challenges.  Really, you should read the article!


xkcd succinctly summarizes the situation.

There are two thought provoking research studies mentioned in the article that we wanted to share.

Moss-Racusin, along with collaborators in the departments of psychology, psychiatry and the School of Management, designed a study that involved sending out identical résumés to professors of both sexes, with a cover page stating that the young applicant had recently obtained a bachelor’s degree and was now seeking a position as a lab manager. Half of the 127 participants received a résumé for a student named John; the other half received the identical résumé for Jennifer. In both cases, the applicant’s qualifications were sufficient for the job (with supportive letters of recommendation and the coauthorship of a journal article) but not overwhelmingly persuasive — the applicant’s G.P.A. was only 3.2, and he or she had withdrawn from one science class. Each faculty member was asked to rate John or Jennifer on a scale of one to seven in terms of competence, hireability, likability and the extent to which the professor might be willing to mentor the student. The professors were then asked to choose a salary range they would be willing to pay the candidate.

The results were startling. No matter the respondent’s age, sex, area of specialization or level of seniority, John was rated an average of half a point higher than Jennifer in all areas except likability, where Jennifer scored nearly half a point higher. Moreover, John was offered an average starting salary of $30,238, versus $26,508 for Jennifer.

— from the NYT Magazine article (emphasis added)


In a frequently cited 1999 study, a sample of University of Michigan students with similarly strong backgrounds and abilities in math were divided into two groups. In the first, the students were told that men perform better on math tests than women; in the second, the students were assured that despite what they might have heard, there was no difference between male and female performance. Both groups were given a math test. In the first, the men outscored the women by 20 points; in the second, the men scored only 2 points higher.

— from the NYT Magazine article.

The first study shows that even today when all things are equal people are treated differently based on their gender. The good news is that the second study shows that its  all in our heads and so we can do something about it!

On the Road with The Schmidt

Like last year, our stalwart Dr. Ralf Schmidt (with invaluable assistance from Lynn Greenleaf and Sophia Morren) led a merry band of OU undergraduate women to the 15th annual Nebraska Conference for Women in Mathematics.

This year’s speakers were Dr. Cathy O’Neil (aka Mathbabe) and Dr. Rekha R. Thomas (aka Professor of Mathematics at the University of Washington, Seattle). 

NCUWM.Web logo

Everyone who goes has a great time.  Indeed, this year the OU contingent was full (with a wait list!) even before we had a chance to announce it!  If you’re interested in going next year, be sure to email Dr. Schmidt early!

But don’t take our word for it.  Three of this year’s participants were Lena Erickson (LE), Sarah Coulson (SC), and Allie Kallmann (AK).  Here’s what they had to say about the trip:

Why did you decide to go to NCUWM?

LE:  I hoped to learn about career options and graduate school and see other undergraduates present their research.

SC:  I wanted to meet and get to know some of my fellow math majors and learn about some of the math programs in the rest of the country. I thought that NCUWM would be a great opportunity to do both of those things.

AK:  I’d had several friends recommend that I go in previous years but was never able to make it work with my schedule, so when I had the opportunity this year, I jumped at the chance! I’m trying to figure out what I want to do with my life, so I thought it would be helpful to find out what other women in mathematics were doing with theirs and see if I could learn from their examples.

What happens at this conference? What did you do there?

LE:  A few main speakers address what they think is relevant for an undergraduate woman in math to know, especially information or advice they wished they had been given as undergrads. Much of the time is spent attending short talks by undergraduate women about research they have done at REUs or with professors at their home universities. Each conference attendee goes to two break-out sessions where there is an opportunity to ask questions to the speakers who know the most about certain topics, like choosing a graduate school. There was also a panel on careers using mathematics, with representatives from the NSA, the US Coast Guard Academy, XBOX Live, and various universities.

SC:  The conference involved a lot of presentations of undergraduate research, as well as panel discussions on topics such as choosing a grad school, finding a career in mathematics, and summer research opportunities. We were pretty much in presentations and at discussions all day, but seeing all of the research that students just a year or so ahead of me have been doing piqued my own interest in research.

AK:  We spent a lot of our time listening to presentations from other undergraduates about their research, as well as getting to know a number of professional women mathematicians. This ranged from the plenary speeches to the panel discussions to one-on-one conversations with, for example, a Program Manager from Xbox Live.

Give 5 words that describe the NCUWM conference.

Screen shot 2013-02-24 at 2.02.29 PM

What was your expectation for the conference? What did it actually turn out to be like?

LE:  I expected it to be formal in tone and purely informational. However, meeting new people was a huge focus of the conference, as well as hearing about older women and their experiences. There was less advice on how specifically to engage in math and more advice about how to navigate the systems of academia and industry, both socially and professionally. The speakers wanted all the undergraduate women in the conference to succeed in math and at life in general, and they did not want students to drop out of math due to lack of social and systemic direction. The undergraduate research presentations gave a good idea of what sort of research is possible at the undergraduate level and how to initiate a research experience.

SC:   I was expecting fewer undergraduate talks and more recruiting from grad school and research programs. The majority of both Saturday and Sunday were actually undergraduate presentations, and I only ran into one recruiter.

AK:  I wasn’t expecting to have near as much fun as I did, honestly. I thought there would be a lot of boring speeches (not true), a lot of mathematics that was over my head (pretty true), and unsociable people forced into awkward situations (kind of true, but we were all in the same boat, so everyone was really cool!). I came home on a SUPER feminist kick because of all of the empowering professionals and successful women there. I also had a blast getting to know the other girls from OU and exploring Lincoln, which is a shockingly neat town.

What was the coolest math thing you heard?

LE:  There was a presentation about Magic Cayley Sudoku Tables, a game/construction like Sudoku that uses Abstract Algebra, so it is more complicated and hence more fun. The undergrad who was creating the game was obviously delighted to be using math to create puzzles.

SC:  I really enjoyed one of the undergraduate presentations on Magic Cayley-Sudoku Tables. Although it didn’t really have any real-world applications, I thought it was pretty neat.

AK:  We spent about 20 minutes on the car ride home talking about the concept of fair division – you know, like with the arguments that you’d have with your siblings over the “bigger half,” which is an exact mathematical measure and an oxymoron. The concept of measuring people’s perceptions with mathematics was really cool for me.

What’s the best piece of information you received at the conference? The thing you will be sure to remember?

LE:  Cathy O’Neil emphasized that when choosing a career, it’s essential that one’s values align with one’s type of work and place of employment. This should be common sense, but most people consider responsibilities, salary, benefits, and location most when choosing a job. It’s rarer and harder to consider whether there will be sufficient feedback, whether one’s incentives will be aligned with one’s coworkers’ and with the goals of the institution, and whether the work is good for the world in general. When thinking about my future, I will likely remember to ask those questions.

SC:   I will definitely remember Cathy O’Neil’s talk about her transition out of academia, the different jobs she has held as a math PhD, and how to find a job in mathematics that makes you happy. I think I’m definitely going to start reading her blog, because she was funny and inspiring.

AK:   I think the biggest thing I came away with was the concept that we shouldn’t let other people’s measurements define our successes, which is something you hear fairly often but really resonated with me over this weekend.

What would you say to someone thinking about going to next year’s conference?
LE:  The conference is immensely valuable to any young woman who wants more direction and who wants to see what sort of research other undergrads are doing.

SC:  I would say that you should be prepared to be exhausted by the end of it, but that you will definitely learn a lot about what being a math major means to you and what implications that has for your future. NCUWM got me started thinking about research, something I hadn’t really considered yet, which has started me on the whirlwind process of applying for REUs. I’m super busy with it, but really excited to get started actually doing something in math outside of my classes. I highly recommend the conference.

AK:  DO IT. Whatever reservations you have, they’re not worth missing out on the opportunity that this presents.  Also, you should present your research. I wish we had had someone doing that.

A talk at this year’s conference:

There's not too many math conferences where the male/female ratio is 1/100! (photo from NCUWM website)

(photo from NCUWM website)