Welcome to Visitor’s Day!

February 21, 2025

Welcome & Introductions

Department Chair: Sarah Reznikoff

Graduate Program Coordinator: Sadie Powell�Graduate Program Director: Andy Norton

Graduate Admissions Chair: Tao Lin

Advising Chair: Eyvi Palsson

GTA Coordinator: Kelli Karcher

Bio page with two pictures and two names and text

Master of Science

• 2 years of GTA/GRA support
• Standard or Interdisciplinary
• Thesis or Non-thesis
• 30 credit hours of coursework
• Thesis, or 2 written prelims, or master’s presentation

Doctor of Philosophy

• Acceptance by Graduate Program Committee, based on good progress
• 4 years of (additional) GTA/GRA support (for students who began in MS)
• 90 hours (courses + research hours + M.S. hours)
• 2 written prelims + oral exam
• Dissertation and defense

DOCTORAL PROGRAM

Compared to undergraduate degrees, the MS and especially the PhD programs are less about coursework and more about research.

Thesis

Preliminary Exams

Coursework

Oral Defense

PRELIMINARY EXAMS

ALGEBRA

MATH 5125-26

ANALYSIS

MATH 5225 (Real), 5235 (Complex), 5214/6255 (Functional)

COMPUTATIONAL MATH

MATH 5424, 5554, 5484, 5544

DIFFERENTIAL �EQUATIONS

MATH 5245 (ODE), 5425 (PDE), Dynamical Systems

Exams offered in

January & August

of Each Year

TYPICAL SEMESTER FOR FIRST-YEAR STUDENTS

• Full load 12 credit hours
• Typical load: 9 credits of courses + 3 credits of research (Math 5994)
• GTA/GRA Assignment
• GTA Training
• Participation in Seminars & Colloquia
• Participation in student organizations (AWM, SIAM, & GSO)
• Developing research interests, including possible conference presentations (travel support provided)

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PROGRESS TOWARD DEGREE

COURSES, COMMITTEE, ETHICS & DIVERSITY REQUIREMENTS

“QUALIFYING EXAM”: PASS 2 EXAMS, AMONG THE 4 OFFERED

“PRELIMINARY EXAM”: RESEARCH PLANS

“FINAL EXAM”: APPLY FOR DEGREE, DEFEND DISSERTATION, SUBMIT ETD

PHD

PROGRESS TOWARD DEGREE

COURSES, COMMITTEE, ETHICS & DIVERSITY REQUIREMENTS

“QUALIFYING EXAM”: PASS 2 EXAMS, AMONG THE 4 OFFERED

“PRELIMINARY EXAM”: RESEARCH PLANS

THESIS, OR PRESENTATION, OR PASS ONE OF THE PRELIM EXAMS

MS

COLLOQUIA & SEMINARS

Colloquia generally Fridays, 4-5pm in Commons Room (reception begins at 3:30)

Attend 6+ seminars or colloquia per semester

These and other department events can be found in the Calendar.

Applied Algebra

Math Bio

Geometry/Topology

Math Education, Algebra, Analysis & Math Physics…

FACULTY RESEARCH AREAS

https://math.vt.edu/�research.html

Andy Norton�Math Education

Epistemology & Psychology of Mathematics

• Framing mathematics as a coordination of mental actions
• Building second-order models of students’ mathematics
• Accounting for the role of general cognitive constructs, such as working memory, in mathematical learning
• Designing quantitative studies to test theories of mathematical development
• Applying knowledge of children’s mathematics, as mathematics, to a better understanding of mathematical concepts, such as the prime number theorem.

Travis Morrison�Number theory & cryptography

Effective methods in number theory

• Easy problems: Can we solve them faster?
• Hard problems: How hard are they?
• (Un)decidable problems: does there exist an algorithm at all?

Sarah Arpin�Number theory & cryptography

• Arithmetic geometry in characteristic p
• Abelian varieties
• Post-quantum cryptography
• Elliptic curves
• Coding theory

Yun Yang

Dynamical systems and ergodic theory

Q: Chaos of Lorenz attractor?

Wenbo Sun

Dynamical system and Ergodic theory

Ergodic Theory in Combinatorics

• Existence of certain patterns in large sets of integer
• Existence of solutions of algebraic equations in large sets of integers
• Existence of certain configurations in large sets in the Euclidean space

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Ergodic Theory in Number Theory

• Averages for multiplicative functions
• Correlation between multiplicative functions and dynamical systems (Sarnak’s Conjecture)
• Arithmetic progressions along primes

3 coloring of K16 without monochromatic triangles

Arithmetic progressions along primes

Omar Saucedo�Mathematical Biology

Focus on the mathematical modeling of infectious diseases

• Avian Influenza
• Explore mechanisms that are contributing to the ongoing avian influenza outbreak.
• Human Behavior
• Determine how human behavior influences disease spread.
• Identifiability
• Examine the model structure to determine the uniqueness of the parameters.
• Stochastic Modeling
• Discover traits for superspreading events.
• Vector-borne Diseases
• Observe disease propagation on a network setting.

Interdisciplinary collaborations across Virginia Tech (Entomology, Population Health Sciences, and more) and across multiple universities.

Michael A. Robert

Mathematical Biology

Mathematical modeling as a tool for investigating infectious diseases.

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• Understanding disease emergence and spread
• Building climate-based models to study dengue emergence in Central Argentina. �
• Developing Early Warning Systems for Emerging Pathogens
• Ensemble models for predicting dengue spread in the Dominican Republic.

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• Connecting physiological models to population dynamics
• How do histamine and serotonin impact malaria transmission?

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• Assessing eco-evolutionary impacts of disease spread and control
• Understanding relationships among dynamics on different time scales.

• Differential Equations
• Difference Equations
• Spatiotemporal models
• Stochastic Modeling
• Statistics & Data Analysis
• Programming & Computation

Tools

• Virginia Tech (Biochemistry, Industrial & Systems Engineering, Statistics, Fish & Wildlife Conservation, Mathematics)
• U.S. Universities (VCU, UTSA, Indiana, U Idaho, U. Washington)
• International (Argentina, Dominican Republic, Colombia, Mexico)

Collaborations

Nicole Abaid

Mathematical biology

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Modeling and control of multi-agent systems

• Agent-based and network models
• Ordinary differential or difference equations
• Inspired by animal group behavior
• Applications to robotic teams

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Current projects:

• Collective energetic regulation in ant colonies
• Cooperative sensing in bat swarms
• Social contagion of stress in human crowds

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I am interested in:

• Data driven methods (and data collection!)
• Or first principles! Or insights from ethology!
• Collaborating!

Giuseppe Cotardo, Hiram H. López, Gretchen Matthews

Coding Theory

Coding theory is the study of mathematical techniques for encoding, transmitting, and decoding information efficiently and reliably.

Approaches, Tools, & Techniques

• Algebraic Geometry
• Combinatorics
• Commutative Algebra

Classical & Modern Coding Theory

• Hamming- and rank-metric codes
• Network communications
• Quantum error correction

Applications

• Code-based cryptography
• Distributed computing - efficiency and security
• Storage - distributed, DNA, complexity theory

Activities & Opportunities

• Applied Algebra Seminar meets weekly during academic year
• ACCESS: Algebraic Coding & Cryptography Seminar Series, twice monthly
• PICS: Post-graduate International Coding Seminar, twice monthly
• ACTiVT and VT-Swiss Workshop in Coding Theory & Cryptography events
• GRAs via collaborations, Commonwealth Cyber Initiative, Hume Center
• Connections with companies and government agencies - internships, placements

Applied Algebra

Research Group

Ionut Farcas:�Computational Applied Math

Research agenda driven by complex and relevant real-world problems:

• Rocket combustion simulations in support of designing the next generation propulsion devices
• Turbulent transport in fusion devices in support of the design and control of optimized fusion devices
• Digital twins for jet engines

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Data-driven modeling:

• Scientific machine learning at scale
• Context-aware machine learning
• Domain decomposition based modeling
• Multi-fidelity modeling

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Uncertainty quantification:

• Forward uncertainty quantification
• Sensitivity analysis
• Uncertainty quantification in model predictions
• Inverse problems

Steffen Werner:�Computational Applied Math

Modeling and simulation of real-world phenomena:

• simulation of complex partial differential equations
• model and complexity reduction
• data-driven surrogate modeling
• closure modeling (first principles + data)

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Control of complex dynamical behavior:

• robustification against modeling errors
• context-aware data informed approaches
• high-dimensional linear/nonlinear matrix equations
• reinforcement machine learning

�Various interdisciplinary applications:

• regulation of fluid behavior,
• vibrational analysis of microchips and drones,
• analysis and stabilization of power networks,
• feedback control of chemical and biological reactors, …

BLACKSBURG, VIRGINIA

Often Listed among Top Places to Live and Top College Towns!

https://www.aier.org/top-20-college-towns-7-blacksburg-christiansburg-radford-va/

https://www.newrivervalleyva.org/news/blacksburg-ranked-among-top-100-small-cities-towns-in-us/

https://dwellics.com/virginia/moving-to-blacksburg

https://money.cnn.com/magazines/moneymag/bplive/2007/snapshots/PL5107784.html

https://usatoday30.usatoday.com/life/lifestyle/2004-03-29-emerging-cities_x.htm

virginia.org

LIVING IN BLACKSBURG

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• Low cost of living:
• Blacksburg Transit is free to students
• Overall cost of living about 5% below the national average
• Safe, clean environment, nestled �in the Appalachian Mountains
• Many recreational opportunities

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• Graduate housing
• Graduate student life
• Graduate school

GRADUATE LIFE CENTER

AT DONALDSON BROWN

A SPACE FOR GRAD STUDENTS

• Housing for over 100 graduate students
• Graduate School offices
• Graduate student organization offices
• Seminar, conference, video conference, and computer rooms
• Career, health, and wellness resources
• Reading and television lounges
• Au Bon Pain coffee shop
• Conveniently located near library, downtown, bus route

WHAT QUESTIONS DO YOU HAVE FOR US?