AfTERMATH

D E PA RT M E N T O F M AT H E M AT I C S BIANNUAL NEWSLETTER | FALL 2017 | VOLUME 17, ISSUE 1

8

9

36

45

21 28

120

35 70

126

210

5

1

15

6

56 126

252

1

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84

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j=1 i=1

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x i,j =

8

i=1

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1 10

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i=1

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0

0

ALAN TURING

÷

4 (4x) + 2 (x) = 72 16x + 2x = 72 18x = 72 x=?

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ax

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+

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PYTHAGORAS OF SAMOS

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c = π·d = 2·π·r

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35 56

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1

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=

17 x 24 = 30 25

2

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∂v ∂x ∂v ∂y

1

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1 4

GOTTFRIED WILLHELM LEIBNIZ 2.56 = 2 + 56/100

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∂u J = ∂x ∂u ∂y

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7

6

ARCHIMEDES OF SYRACUSE

d x e dx

1

5 6

SA = 6s 2

A = s2

EMMY NOETHER

1

ADA LOVELACE

≥

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1 1

2

1

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∞

2

HYPATIA OF ALEXANDRIA

1

∫ sin x dx = -cos x

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c

EUCLID OF ALEXANDRIA

LEONARDO BONACCI

∫a

√

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a

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ELENA CORNARO PISCOPIA

a2+ b2= c 2

SIR ISAAC NEWTON

>

π

Δiπ e +1= 0

x

d = √(x2 - x1)2 + (y2 - y1)2

BERNHARD RIEMANN

SRINIVASA RAMANUJAN

≠

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OMAR KHAYYÁM

A = xr C=2πr

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x

102

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r

525

456 x 0 =

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2

CARL FRIEDRICH GAUSS

t

ERATOSTHENES OF CYRENE

LEONARDO PISANO BLGOLLO

w

| -5 | = 5 101 = 5

84112 > -84112

2 × (3 + 5) = 16 MDCCCL √-1 3.141592653589793238 MATH

®

M essage

from the

C hair

T

his is a natural opportunity for me to welcome all new and returning members of our Department. As the new chair I am glad to renew our ongoing commitments to excellence in research and mentoring at all levels. Our faculty continues to excel in research and training (see p. 6 for some recent highlights), and we continue to provide very high standards of mathematics instruction to our students. You might be aware that our student enrollments are on the rise. This creates challenges, as well as opportunities, that we plan to meet head on. We have maintained focus on student success and our excellent standards of instruction at all levels, provided additional advising support for our majors, and increased our student support programs. I would like to thank the entire department, especially the staff and the department administration for their support and ceaseless efforts in improving the Mathematics Department. In closing, I invite you to take a tour of our newly-redesigned department webpage (www.math.utah.edu) and consider donating to our many scholarly pursuits. I look forward to a successful 2017-2018 academic year.

N ew C hair

and

N ew A ssociate C hair

T

his summer, Peter Trapa completed his second term as Chair of the Department and stepped down. During his tenure in this position, the Department hired ten outstanding faculty members in a wide spectrum of pure and applied mathematics, grew annual research expenditures to about $4M; secured new departmental endowments of about $1.8M; and implemented a number of student-centered initiatives (like enhanced advising and extra lab sections for many lower-division classes) aimed at improving student success in critical gateway courses. We would like to thank Peter for his service over the past six years. Davar Khoshnevisan has been named Chair of the Department. Davar grew up, in different stages of his childhood, in Tehran (Iran), London (UK), and New York, with high school degrees in all (one might say he has a very wellrounded high school education). He joined the Mathematics faculty in 1993 as Assistant Professor. In the past, his hobbies have included pottery and skiing, although time limitations have kept him from these in recent years. He prefers to think about mathematics when he can. Davar has a family of 8 (his spouse, 2 children, a dog, 3 cats, and the very recent addition of a gold fish). Davar is looking forward to working with both faculty and staff toward continuing improvement of the Department. Tommaso de Fernex has been named as an Associate Chair over career-line faculty, a position that is new to our Department. His responsibilities are mainly related to faculty affairs in addition to serving on a number of departmental committees. Tommaso grew up in Italy, and joined our Department in 2005 as Assistant Professor. Besides mathematics, Tommaso likes sports, classical music, photography, drawing, and cooking. He looks forward to sharing some of these passions with his son as he grows up. In his new role, Tommaso is looking forward to the opportunity of workwing closely with the Chair and learning more about the Department, in addition to showing this new position as an asset to the Department leadership.

N ew U ndergraduate A dvisor

N

atasha Carlton has transitioned to working as the second member of our undergraduate advising team and will be working in collaboration with Angie Gardiner. This second advising position has been created, in part, in response to increased student demand. Natasha joined our department in 2015 as the Program Assistant for the Math for America and Master of Science for Secondary School Teachers programs. Natasha has a M.Ed. in Educational Leadership and Policy with an emphasis in Student Affairs from the University of Utah. She has been heavily involved in student development for six plus years and is excited that she will be able to continue to use that knowledge in her new role. Natasha is looking forward to the opportunity of working more closely with undergraduate students and with Angie Gardiner.

Amanda Cangelosi

Instructor (Lecturer) MS in Statistics, Utah State University Research Interests: Math Education

Assistant Professor (Lecturer) Ph.D. 2016, University of Wisconsin-Madison Research Interests: Probability Theory, Stochastic Processes

Bronson Lim

James MacLaurin

Research Assistant Professor Ph.D. 2012, University of Oxford Research Interests: Probability Theory, Stochastic Processes, Math Biology

Gilbert Moss

Assistant Professor (Lecturer) Ph.D. 2015, University of Texas, Austin Research Interests: Number Theory, Algebraic Geometry

Thomas Polstra

NSF Postdoctoral Fellowship Ph.D. 2017, University of Missouri Research Interests: Commutative Rings and Algebras

Ron Reeder

Adjunct Assistant Professor Ph.D. 2011, University of Utah Research Interests: Statistics Tenure Track Position Department of Pediatrics

Dong Wang

Assistant Professor (Lecturer) Ph.D. 2017, Hong Kong University of Science and Technology Research Interests: Numerical Analysis

Lei Wu

Research Assistant Professor Ph.D. 2017, Northwestern University Research Interests: Algebraic Geometry

Master Students: (MA, MS, M.Stat. & MS.T.) Blair Brook Jennifer Call Merry Carney Merilee Gandy Sean Groathouse Colton Grainger Emre Gul Heather Hardy Rebecca Hill Jessica Humphrey Jacob Kettinger Gray Marchese Elena Nazarenko John Nordstrom Chanel Roe Rebecca Stevens Lu Tian Josh Tracy Charlotte Whiteside Kali Wickens David Winkler Lin Zhang

Who Joined the Department 2017 - 2018

Research Assistant Professor Ph.D. 2017, University of Oregon Research Interests: Algebraic Geometry

Amanda Alexander (Western Washington U.) Donald Chacon-Tayler (U. of British Columbia) You-Cheng Chou (National Taiwan U.) Chengyu Du (Nankai U.) Justin Eastman (Colorado State U.) Rebekah Eichberg (Indiana U. - Bloomington) Seungsu Lee (Yonsei U.) Zexin Liu (Beihang U.) Jacob Madrid (U. of Utah) Kees McGahan (Willamette U.) Mitchell Meyer (Oklahoma State U.) Curtis Miller (U. of Utah) Ryleigh Moore (Boise State U.) Vaibhav Pandey (NISER) Kimberly Truong (Brown U.) Yiming Xu (Sichuan U.) Jose Yanez (Pontifical Catholic U. of Chile) Ryeongkyung Yoon (Ohio State U.)

People

Christopher Janjigian

Ph.D. Students:

F aculty

I

f you ask most people to imagine the lifestyle of a mathematician, chances are that mental picture will not include traveling on an icebreaker through the Western Weddell Sea off the coast of Antarctica! For Dr. Kenneth M. Golden, however, this is an essential part of his life’s work: the mathematical study of sea ice and climate. To say Ken’s research is ‘interdisciplinary’ would be an understatement; his work has utilized methods from such varied fields as fractal geometry, composite materials, remote sensing, functional analysis, microbial ecology, and statistical physics. He refers to the strategy of transferring mathematical methods between unrelated areas of science as “cross-pollination,” which cultivates new ideas and areas of study.

Ken’s excitement is contagious when speaking about his work, evidence of a lifelong passion for his field. Born and raised in College Park, Maryland (a few minutes from the university), Ken had his first taste of research while participating in an NSF Summer Science Training Program at the Institute for Arctic and Alpine Research in Colorado after the 11th grade. His work involved coring peat bogs for paleoclimate analysis and studying the physics of snow melt. This led to work the following school year with Jay Zwally of NASA, where he began to study Antarctic sea ice using a combination of mathematics and satellite imagery. Ken then attended Dartmouth for his undergraduate studies, where he received his B.A. in mathematics and physics. During this time, he began working under Steve Ackley of CRREL (Cold Regions Research and Engineering Laboratory), where he focused on methods of measuring the thickness of sea ice. This culminated in Ken’s senior year with his first trip to Antarctica aboard the USCGC Polar Sea. This was one of the first expeditions into the Western Weddell Sea since Ernest Shackleton’s ill-fated voyage in 1914. It would be the first of many such trips for Ken, whose globe-hopping research has taken him to six continents, including seven trips to Antarctica and eleven trips to the Arctic. Dr. Golden received his Ph.D. in mathematics from NYU’s Courant Institute; his thesis was Bounds for Effective Parameters of Multicomponent Media by Analytic Continuation. He has gone on to publish over 70 papers across a variety of fields (including six papers with his college mentor, Steve Ackley). He was one of the first researchers to combine rigorous mathematics with the observation that sea ice should be treated as a multiscale composite material when considering its role in the Earth’s climate system. Dr. Golden has received numerous grants and awards throughout his career that not only bring attention to his work, but to the University of Utah and the Mathematics Department as a whole. In total, Ken has been part of 28 grants, responsible for over $14 million in funding. In fact, Ken, along with co-PIs Elena Cherkaev and Tom Alberts, received a new NSF grant this year to study random matrix theory in the context of homogenization for composites. Ken was the Guest of Honor at the Institut des Hautes Études Scientifiques (IHÉS) Gala hosted by the French Ambassador to the US on November 18, 2013. He is also an Inaugural Fellow of the American Mathematical Society, a SIAM Fellow, and has received the University of Utah’s Distinguished Teaching Award (the U’s highest

S potlight : K enneth G olden teaching award), to name just a few of his prestigious awards. Ken has also been invited to speak at various prominent venues. He has given the SIAM Invited Address at the Joint Math Meeting (AMS-MAA-SIAM), the Houghton Lectures in Earth, Atmospheric and Planetary Sciences at MIT, and has even presented his research on sea ice and climate change to the US Congress on three separate occasions. However, perhaps the one award that most stands out is his election as a Fellow of the Explorers Club, an international multidisciplinary professional society dedicated to the advancement of field research and the ideal that it is vital to preserve the instinct to explore. Ken is only the fourth math professor since 1904 to become a member of this elite society, which includes astronaut Neil Armstrong, test pilot Chuck Yeager, Mount Everest conqueror Sir Edmund Hillary, and primatologist Jane Goodall. Ken also serves as a valued research mentor and advisor to undergraduates, masters students, Ph.D. candidates, and postdoctoral fellows — fifty-eight university students and postdocs in total, with majors of the undergraduates spanning eleven departments in the Colleges of Science, Engineering, and Mines and Earth Sciences. One former student once commented: “By treating me more like a colleague than a student, Dr. Golden aided my research successes throughout my undergraduate career.” Perhaps most notable is Ken’s mentorship of nine high school students, giving them an opportunity to publish even before deciding on an undergraduate program. This has proven to be a great way to payforward the opportunity Ken had to work on research at an early age. Ken also values speaking at general STEM gatherings, where the “cross-pollination” of ideas benefits everyone in the audience. Such experiences led Elena and Ken to investigate the similarity between the structure of sea ice and bone tissue, leading to a new way of electromagnetically monitoring the progress of osteoporosis. Dr. Golden was recently honored with the title of Distinguished Professor of Mathematics for his outstanding accomplishments in research, teaching, and community outreach. Ken’s career path and success has stemmed in part from his belief that “mathematics is the operating system of science and engineering,” like Unix, Mac OS or Windows. As a result, he would be hard pressed to advise a future scientist not to pursue classes in higher level mathematics. However, he also advises students to find something they love to do. Combining these two pieces of advice leads to the following feedback loop Ken believes applied mathematicians should follow: find an important real-world problem, develop the mathematics to solve it, see what new real-world problems and mathematical questions are revealed, and repeat!

D e p a r t m e n t D i s t i nc t i o n s

F aculty Department of Mathematics Awards

Linquan Ma (Don H. Tucker Postdoctoral Fellow Award) Maxence Cassier & Ioannis Konstantoulas (Outstanding Postdoc Award) Peter Alfeld & Maggie Cummings (Faculty Undergraduate Teaching Award)

University Awards

Kelly MacArthur (Excellence in General Education Teaching Award) Karl Schwede (Presidential Scholarship)

Other Awards

Mladen Bestvina (2017 Simons Fellow) Christopher Hacon (Elected to American Academy of Arts and Sciences) James Keener (John Jungck Prize of Excellence in Education from the Society for Mathematical Biology)

S taff Department of Mathematics Awards Mary Levine & Paula Tooman (Outstanding Staff Award)

University Awards

Pieter Bowman (30 Years of Service) Angie Gardiner (20 Years of Service) Kristina “Chi” Ong (20 Years of Service)

G raduate S tudents Department of Mathematics Awards

Heather Brooks (T. Benny Rushing and Gail T. Rushing Fellowship) Gregory Handy & Derrick Wigglesworth (Outstanding Graduate Student Award) Anna Romanova, Franco Rota, Weicong Su, Qing Xia, & Chuanhao Wei (Departmental Summer Research Fellowhip)

University Awards

Sean McAfee & Anna Romanova (University Teaching Assistantship) Priscilla Elizondo (University Graduate Research Fellowship)

U ndergraduate S tudents Department of Mathematics Awards

Joshua Peterson (Calvin H. Wilcox Memorial Scholarship) Cynthia Munoz (Junius John Hayes Diversity Scholarship) Miriam Galecki & Thomas White (Junius John Hayes Endowed Scholarship) Justin Francis (The Golden Scholarship) Veronica Riker (D. Keith Reed Memorial Scholarship) Sarah Melancon (Susan C. Christiansen Memorial Scholarship) Brendan Black (Thomas Andrew Hurd Mathematics Scholarship) Zachary Basta & Shravan Parthasarathy (Saxton Scholarship) Weston Barton (C. Bryant and Clara C. Copely Scholarship) Whitney Bitner, Charlotte Blake, Han Le, Shalynne Orth, Travis Tiner, & Cate Youatt (Continuing Departmental Scholarship) Emma Fine, Sarah Hall, Staci Jewkes, & Scott Neville (Mathematics Department Scholarship) Ethan Lake (J.L. Gibson Senior Award) Matthew Bernstein (Putnam Award) Matteo Sogne & Scott Neville (Undergraduate Problem Solving Contest Winner & Student Representative)

College of Science Dean’s Office Awards

Irina Slaughter & Elena Nazarenko (Joseph T. Crockett Scholarship) Cari Winger (Don and Rebecca Reese Science Teaching Scholarship)

A C C E S S S ummer M ath P rogram

D

T

his summer, the Department of Mathematics was once again proud to be involved with the ACCESS Program for Women in Science and Mathematics. This year, Braxton Osting and Stefan Patrikis each taught for one week out of the seven week program. During their time studying mathematics, the women were introduced to “Symmetry” in a hands-on introduction to group

theory with an emphasis on the symmetries of polyhedra and of wallpaper patterns. They also studied cryptogrophy by introducing public key cryptography, which cleverly relies on the fact that it is difficult to factor the product of two large prime numbers. These ideas were then used to make a cryptocurrency, dubbed “ACCESS coins,” a simplification of bitcoin.

for

H igh S chool S tudents

uring the summer, twenty Utah high school students spent four weeks at the Department’s Summer Mathematics Program, working their way through an intensive introduction to number theory. Our core commitment was and is that any bright and curious student, almost regardless of mathematical preparation, can experiment with basic arithmetic, feel the excitement of conjecturing, and know the profound satisfaction of being the origin rather than the receptacle of serious mathematics. This is what the students achieved through their extraordinarily diligent and enthusiastic work on each day’s difficult but carefully-paced problem set; in all, these sets gradually led the students from the most fundamental notions (congruence, factorization, etc.) to some of the gems of classical number theory (such as Fermat’s two squares theorem and quadratic reciprocity). Stefan Patrikis served as Program Director, and his thoughtful leadership and teaching truly enhanced the learning experience for the students. Throughout the summer, our thoughtful and devoted counselors — Michael Bolton, Christian Klevdal, Sean McAfee, and Allechar Serrano López — gave the students nudges as needed in the right direction, taught them to write proofs, and critiqued their daily written work. Outside of the classroom, Aryn DeJulis organized every aspect of the program, from advertising it across the state to arranging daily lunches for the students and staff. Finally, we greatly enjoyed guest lectures from Ken Golden, Christel Hohenegger, Anurag Singh, and Kevin Wortman, who gave the students, alongside the deep focus of the number theory course, a taste of the awesome breadth of mathematics.

I

L ife as an I nternational G raduate S tudent

t is no secret that almost every Math Department has international students. We are coming from different countries with more or less the same goals – to study mathematics abroad with new possibilities and challenges. At first, it is not easy to make a switch in your mind from your native language terminology to English. Names of the theorems, notations, and styles in general might be different from what you are accustomed to. Nevertheless, you get it with time. You stop translating everything and start thinking in English all the time. At some point, English becomes the “doing math” language. As an international graduate student, I feel the most interesting things happen when you start teaching mathematics to others. There are always many choices you have to make when it comes to bringing your international experience to the classroom. Are your ways of learning and understanding math better? Will local students accept them? At the end of the day you realize that everything will work out – studying, teaching and acclimatization. What is paramount and invaluable is having nice and caring people around you. Our Department has a truly supportive environment with people ready to answer your questions and even to just talk. Having a positive atmosphere means a great deal for everyone at the Department, but especially for international students. 155 South 1400 East, JWB 233 Salt Lake City, UT 84112-0090 Phone: (801) 581-6851 www.math.utah.edu

Connect With Us

Af TERMATH Content Selection Natasha Carlton Aryn DeJulis Davar Khoshnevisan Nat Smale

Editors

Natasha Carlton Aryn DeJulis Ken Golden Gail Howick Mary Levine

Layout & Design Aryn DeJulis

Photography & Illustration Natasha Carlton Todd Collins Photography Aryn DeJulis Karen Frey Ken Golden Rebecca Hardenbrook Alison Kohout Jan Lieser David Lubbers Della Rae Riker

Contributing Writers Natasha Carlton Aryn DeJulis Gregory Handy Iuliia Inozemtseva Sean McAfee Braxton Osting Stefan Patrikis

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