We have a great group of students this year from all over the country. Each student brings their personality and specialty to the team. We hope that all student will use their background to the best of their ability to help the research teams produce interesting findings. We want to share with you some of the brilliant minds that help make up the team.

- Alejandro R. Aponte from Florida international University
My name is Alejandro R. Aponte, and I am a physics major with minors in math andcomputer science. I currently attend Florida International University, where one of my biggest academic interests is interdisciplinary research. I used to be a Bachelor of Science in Politics ,Philosophy and Economics (Logic and Game Theory) at Northeastern University. However,when I found the intersectionality of physics, math, and computer science, it became my passion. This intersectionality, which is formally known as quantum computing, is what interests me the

most in academia. The main reason why I am interested in Quantum Computing is because I

would like to leave a legacy for future generations. Technology has been the gift that previous generations have left us, so I aspire to continue with the tradition. Some of my other interestsinclude sports, service work, and music. - Catherine Fraga from Johns Hopkins University
My name is Catherine Fraga (she/her); I am a second-year student at Johns Hopkins University pursuing a B.A in Mathematics and Psychology. I am particularly interested in finding ways to merge mathematics and biology. I have worked in a biophysics lab through a summer REU program called STROBE, where I did imaging analysis on cardiomyocytes to study their development. I am currently working in a biostatistics lab with the Johns Hopkins Hospital, where we are building a model to improve mortality outlook on infants with congenital heart diseases. In the AMRPU I hope to research topics in algebra and topology, and their applications to phylogenetic trees. Outside of the classroom, I volunteer with a community outreach program based inside a hospital with a dense low-income immigrant population. I hope to go into the medical field and gather enough experience through my mathematical background and lab work to bring a new perspective into medical research.

- Daniel Cabanez from Florida International University
Hello, my name is Daniel Cabanez, I am an undergraduate student at Florida International University studying mathematics and I find some of the formalities in mathematics such as formal characterization of mathematical objects to be interesting. Though intuitively questions like “why a circle is not a line” may seem obvious the techniques employed to explicitly prove this fact are not. For example, the difference between a circle and a line is not obvious in all contexts because set theoretically there is a bijection between the two and thus a circle would be equivalent to a line as a set. One method that is often used to characterize mathematical objects is to construct an invariant from the object that would allow the object to be differentiated from. Homology theories are a potent collection of such techniques that allow the construction of a chain of invariants that allow characterization of mathematical objects. I am extremely honored and excited to take part in this REU to study specific homology theories that offer a potent and powerful method of characterization. Specifically, I am excited to calculate and study the Algebraic de Rham and Crystalline cohomology of the elliptic curve and of projective space under talented graduate students and professors.

- Diana Nguyen Son from University of Tennessee, Knoxville
My name is Diana Nguyen Son, and I am working to complete my undergraduate degree in Applied Mathematics and Computer Science at University of Tennessee, Knoxville. Since 2018, I’ve made efforts to grow and diversify my knowledge of mathematics and coding skills. While my challenging coursework helps to improve understanding, my on-campus job as a tutor and supplemental instruction leader helps to sharpen the saw of older courses. I believe math is a vertical education, so I am continuously looking to strengthen my foundation while building on my capabilities as a mathematician and programmer. Currently, I am participating in a research program for Applied Mathematics at FIU. Specifically, I am looking forward to conducting research involving PDEs and Numerical Analysis, and in doing so, I feel I will be better prepared to achieve my goals of furthering my education with a graduate or masters program in Applied and Computational Mathematics.

- Gia Azcoitia from Florida International University
My name is Gia Azcoitia and I am currently a sophomore, soon to be junior, majoring in

electrical engineering at Florida International University. I have realized my passion for math

during the last few semesters of my college career. My passion for math has culminated in me

working as a Calculus 2 Learning Assistant, a job I have come to enjoy deeply. My career goals

are quite obscure to me at this point in time. I have full intention of remaining in academia after I have completed my undergraduate degree, with the intention and hope to procure a PhD in

applied mathematics. With this in mind, the areas of study that currently appeal most to me are

nonlinear PDE. If you are interested in contacting me, my email is gazco002@fiu.edu. - Hannah Wubben from Loras College
My name is Hannah Wubben, and I am obtaining a B.S. in Mathematics and Computer Science at Loras College. Recently, I have been conducting research surrounding the mathematics of animated films. This process includes digesting a number of key animation techniques including simulation, character modeling and methods for modeling objects in motion and in collision with one another. The ultimate goal is to program a short, computer animated video clip using these mathematical methods. Currently I am attending an REU in Applied Mathematics with a focus in Partial Differential Equations. I am eager to participate in small research groups over the summer. My goal is to some day become a software engineer where I will continue to work with mathematics in animation movies. Hannah's participation in the REU has gotten the attention of some local media. One article from The Galena Gazette and another from Loras Daily.

- Isaac Friedman from Otterbein University
My name is Isaac Friedman, I graduated as valedictorian with an Associate’s of Science degree from Columbus State Community College. I am currently pursuing a Bachelors of Mathematics with a minor in computer science at Otterbein University. During my time at Otterbein, I have taken courses in advanced undergraduate math subjects such as multiple courses in real analysis, abstract algebra, graph theory, and topology alongside various computer science courses. I have done research pertaining to Fourier Analysis and the Continuous Wavelet Transform while at Otterbein. I look forward to expanding my research to include their applications to partial differential equations during my time at the AMRPU at Florida International University. My aim is to receive a PhD in analysis and use my experience to teach others about the beauties of mathematics as a professor. I also enjoy volunteering, and I have logged over 500 hours in mathematics tutoring while in high school and college.

- Jaclyn Pascual from Florida International University
My name is Jaclyn Pascual (she/her) and I am an undergraduate student pursuing a B.S in Mathematical Sciences at FIU. As a freshman, I participated in a year-long Undergraduate Research Opportunity Program (UROP) that consisted of seminars meant to expose young undergrad to what research entailed. From this, I developed an interest in exploring my own research interests. That year, I had the opportunity to have a mentorship and research experience in biomathematics. In particular, my biomathematical interest is in mathematical modeling in epidemiology and public health. My other research interests are in algebra and topology. In AMRPU, I hope to explore how to use and apply algebra and topology.

- Marcos Masip from Florida International University
My name is Marcos Masip (he/him), I am a protestant Christian who is interested in Theoretical Partial Differential Equations. I graduated from Miami Dade College with an Associates Degree in Mathematics. Currently I am working towards my BS in Comprehensive Mathematics at Florida International University and aim to receive a Doctorate’s Degree in mathematics in the near future. I’ve been involved in research related to biology and chemistry, helping to develop polymer beads in order to make the transfer of drugs to certain parts to the body system more manageable. At the moment, my interest is in understanding nonlinear partial differential equations and its solutions through different methods. If you would like to contact me, my email is godisfirstintheworld@gmail.

com. - Minato Hiraoka from Wake Forest University
My name is Minato Hiraoka and I am a rising junior at Wake Forest University studying Applied Mathematics and Computer Science (expected Spring 2022). During my time at Wake Forest, I partook in a research-training group for "Algorithmic Music Composition," where I developed stochastic models for music compositions and assessed ways to reduce complexities to implement these models. I am also an avid mathematical modeler and have participated in various modeling competitions such as COMAP's Interdisciplinary Contest in Modeling. This year, out of over 6000 teams globally, our team was ranked in the top 5 submissions from the USA for our specific problem. Recently, I began working on my undergraduate thesis project: "Optimal Implementations of Non-Pharmaceutical Interventions on Adaptive Networks," on models for infectious diseases, which I am very ecstatic to work on!! Through the AMRPU at FIU, I hope to gain a new palette of skillsets in mathematical computation and analysis that will facilitate my future research projects. My primary goal is to grow to be a mature researcher who is prepared to pursue research in graduate school; to develop rigorous mathematical frameworks across a variety of fields. As a long-term goal, I hope to become an effective communicator across disciplines and apply quantitative methods to a wide range of problems.

- Monica Alvarez from University of Florida
Hi, my name is Monica Alvarez and I am an undergraduate student at the University of Florida pursuing studies in Mathematics and Actuarial Sciences. I am eager to participate in research in topics related to applied statistics, quantitative research, analysis of financial data, probability theory and more. Through this opportunity, I am able to explore my love for mathematics and I aim to implement the knowledge I will gain throughout all of my academic endeavors. I look forward to applying my analytical and strategic ways of thinking to important research and am thrilled to be working with such highly respected peers at this university. Ultimately, my goal is to become a successful actuary where I will devote myself to my passion for mathematics in the world of business.

- Peter Kauphusman from Winona State University
I am Peter Kauphusman, an undergraduate student enrolled at Winona State University in Winona, Minnesota. Currently I am pursuing a B.S. in mathematics and have fulfilled the requirements for a minor in history. My main mathematical interests include differential equations and their explorations into mathematical biology, as well as reading historical mathematics treatises. I am especially eager in furthering my understanding of chaotic systems and their possible insights into mathematical modeling. The intersection of mathematics and history that I would enjoy working on the most is a compilation of similar operational processes, for example regional/cultural/time differences in addition, multiplication, calculus, etc. Honest effort and the courage to try again has allowed mathematics to inspire discipline and engagement through myself and those around me since my first Calculus course in the fall of 2019.

- Troy Roberts from University of Alabama
My name is Troy Roberts and I'm a rising senior at the University of Alabama. My first two years I was a geology major and performed research in a dendrochronology and paleoclimatology lab. As much as I loved studying the Earth and the pressing issues of climate change, I couldn't ignore my true passion - mathematics. After exposure to ideas of logic and analysis I was hooked. At this REU I plan to dig deeper into Fourier Analysis and Lebesgue spaces. I'm most interested in analysis and in particular, the construction of methods to solving PDEs. I will be graduating with a B.S. in pure math with minors in chemistry, physics, and geology in the spring of 2022 and master's in mathematics the following year. I plan to stay in academia to teach and research as a professor.

- Vladyslav Drezels from Florida International University
My name is Vladyslav Drezels, I am an undergraduate student at Florida International University. At the Research Experience for Undergraduates I see myself on the Algebraic/Topological track, which intersects with my personal career interests in Algebra and Combinatorics. In the project we are studying algebraic geometry using methods from homological algebra. At this point I learnt the theoretical apparatus consisting of topics from category theory including functors, pre-sheaves, sheaves, exactness of complexes and homologies. In particular, I have seen several calculations of Cech, Hyper and Algebraic De Rham cohomologies. I am happy and inspired because of this opportunity to combine studying mathematical questions and methods new to me and understand doing mathematics from more professional viewpoint.

Let's find out more about the wonderful graduate students helping with the project. With plenty of insight into the world of research, the graduate mentors help the AMRPU students enter the world of research with care and grace. The hard work that the graduate students dedicate cannot be understated, and the quality of the program rests in the hands of the charismatic and knowledgeable graduate mentors.

- Alex Rodriguez, Technical Support and Graduate Mentor
My name is Alex David Rodriguez, I graduated with a B.S. in Mathematical Science from Florida International University (FIU) in the Summer of 2020. As an undergraduate, my research was focused on Biophysics and Applied mathematics. Where I modeled the contraction rate of heart cells and studied the behavior of solutions to the stochastic nonlinear Schrodinger equation (SNLS). Currently, I am a Ph.D. student at FIU and my research interests lie in dispersive partial differential equations (PDE's). Apart from my research; I was an active part of the Math club E-board as an undergraduate, and this year I founded a directed reading program at FIU with the goal of introducing undergraduate math majors to research. Recently I was awarded an Honorable Mention for the NSF graduate research fellowship for my research proposal in PDEs and activity in mentoring and tutoring undergrad and high school students.

- Eddy Perez, Graduate MentorHi, my name is Eddy Perez. I'm a Ph.D. student at Florida International University studying Applied Mathematics. My favored branches in Math are Complex Analysis, Differential Geometry, and Partial Differential Equations. The main topic of my research is the structure of the Einstein Field Equations in Hermitian/Kahler manifolds. My goal in this research topic is to identify the existence and uniqueness of these equations' solutions, given initial/boundary conditions and the metric of the manifold.
- Giancarlo Sanchez, Graduate MentorMy name is Giancarlo Sanchez and I'm currently pursuing a Ph.D in Applied Mathematics at FIU. My research interests include Deep Learning, Topological Data Analysis, and Financial Mathematics. Outside of academics, I have a passion for cooking Caribbean cuisine and writing love songs available only for my Patreon subscribers. After a long day of studying mathematics, I enjoy playing a
*relaxing*game of Overwatch with some of the other graduate students who are also hard stuck in Gold. - Ginelle Gonzalez, Graduate MentorMy name is Ginelle Gonzalez and I’ve been studying mathematics for as long as I can remember, but I got my bachelors at FIU in math just a year ago. Everyone in my family thought that was the end of the line for me, but we all know that research never ends. So now I’m in the phd program and happily working for FIU and excited to be doing research on the structure and behavior of arteriovenous malformations with the goal in finding a way to relieve the pain in others like me with this rare disease.
- Iryna Petrenko, Graduate MentorMy name is Iryna Petrenko. A while ago being a high school student I became interested in mathematics and science. In 2007 I received a bachelor degree in Automation and Computer Integrated Technologies from Odessa National Academy of Telecommunications, Ukraine. In 2008 I completed my Master degree in Automation and Computer Integrated Technologies at the same place. While working on the master thesis I had a few engineering problems and the solutions were done by applications of mathematical optimization. After graduation I decided to dedicate my life to mathematics and science. I got an Instructor position at the Department of Computer Science. Working and continuing my research there I found that the mathematical methods of solution engineering problems are more interesting for me than the problems themselves. That is why I have applied to the Master of Science in Applied Mathematics program at Georgia Southern University. Studying at that program I were working as TA and realized that teaching of mathematics is the passion of my life. I obtained my Master degree in 2017. Now I’m continuing my research and doing my PhD here at Florida International University. My field of interest is PDE, dynamical system, numerical methods, methods of optimization.
- Jose Medel, Graduate MentorI am interested in geometry, the methods I use to study geometry are based on category theory and algebra e.g schemes, commutative algebra, and homological algebra. I appreciate the opportunity that the REU at FIU has given me for bringing me closer to brilliant undergraduate students so I can inspire them to pursuing mathematics, specifically algebraic geometry. In mathematics it is crucial to have characterizations of its objects, and in geometry we are trying to characterize “form.” Cohomology theories are extremely potent techniques to characterize topological spaces in general. The current research project is using certain cohomology theory approaches to study elliptic curves, which are important, for example, in cryptography.
- Justin Wisby, Technical Support and Graduate MentorMy name is Justin Wisby (he/him). I got my B.S. in abstract mathematics from The University of Michigan -- Flint in 2018. Since then, I have worked as a programmer and mathematics curriculum developer for primary school. Recently, I have been working on my degree at FIU for just over a year. My future degree is a Masters in Mathematical Sciences focusing on research projects involving combinatorics. I am eager to contribute to our group of students over the next couple of weeks as their technical support. This group of students has great potential so I am excitingly waiting to see the results this summer of hard work brings. Until that time comes, I will be focusing on my studies and research to pass the time. I aim to obtain my Ph.D. in abstract mathematics with the goal of one day becoming a university professor to help others learn how fun mathematics can be.

If you would like to know more or reach out, check out my website jwisby.com - Luis Caicedo, Graduate MentorMy name is Luis Caicedo Torres. I am currently a Ph.D. student at Florida International University (FIU) in Applied Mathematics. My research interests lie in partial differential equations, spectral theory of differential operators, and their applications. One interesting idea to explore is the underlying structures of different differential operators in order to discover behavior that is similar between them. This analysis can help us make meaningful conclusions in mathematical physics and machine learning in order to unify a lot of theory. I hope to bring excitement for the applications of the rich theory of many fields to other mathematicians. I look forward to working with the set of bright students the AMRPU will bring together as I think that teaching and training the future generations of mathematicians is as important as research itself.
- Mymuna Monem, Graduate MentorMy interest in Statistics and Mathematics motivated me to pursue a BS and MS degrees in Statistics,

Biostatistics and Informatics from the University of Dhaka, Bangladesh. I have completed my second MS

degree in Mathematics with concentration in Statistics from Mathematical Sciences department at

Georgia Southern University (GSU), Statesboro, in Georgia, USA. Now I am in a PhD program at FIU. My

research interests in Mathematics based on Statistics lie in the general areas of Survival Analysis,

Bayesian Statistics, Mathematical Biology, Regression Analysis, and Stochastic Modeling of

epidemiological processes. I love teaching. In my graduate assistant and adjunct instructor role, I

assisted undergraduate students with problem solving, homework and projects in courses such as

Survey of Calculus, Calculus I, Calculus II, College Algebra, Trigonometry, Introduction to Statistics,

and Probability etc. Hope to continue the good work and make myself qualified to become a

researcher and a consultant in the area of Mathematics and Statistics.