Hello! I am a recently minted mathematics Ph.D. from Virginia Tech. I am forever grateful for the countless opportunities to grow as a teacher, researcher, and person over the last several years at VT. Please explore this site to learn more about me, my values, and my experience.
Curriculum vitae, Teaching Statement, Research Statement, DEI Statement
Email: vdaniel1@vt.edu
YouTube Channel: Chillaxiom
University: Virginia Tech
Advisor: Dr. Gretchen Matthews
Dissertation: Linear exact repair schemes for distributed storage and distributed matrix multiplication
Setting: Taught 8 sections up to 70 students per section.
Topics: Symbolic logic, proofs, contradiction, induction, set theory, cardinality, etc.
Effectiveness Score: 5.7/6 vs university average 4.8/6
Student Quote: "Best professor I've had at VT! Explains discrete math really well and has this energy about him where you sense he cares for his students and their ability to learn the material."
A distributed storage system is a network of storage nodes over which we can store a single data file. Ideally, the data will be stored such that if one or multiple nodes fail, the remaining nodes can be used to recover the lost information. My work with coding theory and interesting multivariate polynomials is directly applicable to this problem and I have made the following contributions.
Publications
H. H. Lopez, G. Matthews, D. Valvo. Erasure repair for decreasing monomial-Cartesian and augmented Reed-Muller codes of high rate. IEEE Transactions on Information Theory, 2022.
H. H. Lopez, G. Matthews, D. Valvo. Augmented Reed Muller codes of high rate and erasure repair. IEEE International Symposium on Information Theory, May 2021.
D. Valvo. Repairing Cartesian Codes with Linear Exact Repair Schemes. M.S. thesis, Dept. of Math, Virginia Tech, May 2020
Invited Talks
D. Valvo. Linear Exact Repair Schemes for Multivariate Evaluation Codes. PostGraduate International Coding Theory Seminar (PICS). Online (March 2022).
D. Valvo. Repairing High-Rate Augmented Reed-Muller Codes. Society for Industrial Applied Mathematics (SIAM). Online (August 2021).
D. Valvo. Augmented Reed-Muller Codes of High Rate and Erasure Repair. IEEE Symposium on Information Theory (ISIT). Online (May 2021).
University: Virginia Tech
Advisor: Dr. Gretchen Matthews
Thesis: Repairing Cartesian Codes with Linear Exact Repair Schemes
Setting: Taught 1 section of 40 students
Topics: Integration, integration by parts, 3D integration, trig sub, partial fractions decomposition, work, center of mass, sequences, series, etc.
Effectiveness Score: 5.68/6 vs university average 5.0/6
Student Quote: "There are very few teachers who have helped my learning as much as Mr. Valvo. He is extremely enthusiastic about his material and loves explaining the material in easy-to-understand ways. When Mr. Valvo was teaching, I felt like he truly cared about my learning and wanted to help me understand the material..."
A distributed matrix multiplication scheme is one in which the product of matrices A and B is computed in parallel utilizing N helper servers. A T- secure distributed matrix multiplication scheme is one in which any T helper servers cannot collude to obtain any information about A or B. My work with coding theory and interesting multivariate polynomials is again directly applicable to this problem and I have made the following contributions.
Publications
H. H. Lopez, G. Matthews, D. Valvo. Secure MatDot codes: a secure, distributed matrix multiplication scheme. Information Theory Workshop, November 2022.
Invited Talks
D. Valvo. Secure Matrix Multiplication Schemes via Locally Recoverable Codes. Joint Mathematics Meeting, AMS Special Session on Coding Theory for Modern Applications (January 2023).
D. Valvo. Secure MatDot codes: a secure, distributed matrix multiplication scheme. Information Theory Workshop. Online (November 2022)
University: Virginia Tech
In-Major-GPA: 3.88
Overall GPA: 3.74
Awards: Traditional Math Senior of the Year (2017-2018)
Setting: Taught 1 section of 40 students
Topics: Limits, continuity, differentiation, implicit differentiation, related rates, and the fundamental theorem of calculus
Effectiveness Score: 5.33/6 vs university average 4.81/6
Student Quote: "He is one of the best calculus teachers I have had. The amount of enthusiasm made calculus fun and more rewarding. He is also very easy to approach and gives very helpful advice and has many openings to contact if there are issues."
My main research focus is coding theory. Coding theory is the study of transmitting information effectively and efficiently in the presence of errors. I have specifically developed expertise in the following areas.
Polynomials over finite fields
Multivariate polynomials over finite fields
Reed-Solomon codes
Reed-Muller codes
Evaluation codes
Linear exact repair schemes