My research interests lie in Coding Theory, Error correcting codes, Cryptography, Complex Geometry, Differential Geometry, Algebraic Geometry, Complex Analysis. I also have interests in Mathematics Education---particularly on innovative pedagogy, effective learning strategies, and different technologies used for instruction and assessment.
Publications and Pre-prints:
A. Álvarez, K. Planadeball Fernandez, J. Sinobio, C. Williams. Integrating Students-as-Partners into College-Level Mathematics Courses. Internationaal Journal for Students as Partners. 10, no. 1, 2026. (Link)
G. Terra Bastos, A. Álvarez, C. Williams. A Construction of Infinite Families of Self-Orthogonal Quasi-Cyclic Codes Using Constituent Codes. Submitted. 2025. (Also see: arXiV:2511.02813.)
K. Aguilar, A. Álvarez, R. Ardila, P. Sanchez Ocal, C. Rodriguez Avila, A. Várilly-Alvarado, Locally recoverable algebro-geometric codes from projective bundles. Accepted. 2025. To appear in Des. Codes Cryptogr. (Also see: arXiV:2409.04201.)
M. Andalibi, A. Álvarez, C. Williams, J. Adams, Bridging Abstract Mathematics and Practical Engineering Design: A Pre-Capstone Project to Enhance Learning and Cultivate Entrepreneurship, ASEE PSW Annual Conference, Cal Poly Pomona Pomona, California, 2025.
G. Terra Bastos. A. Álvarez, Z. Flores, A. Salerno. A Construction of Optimal Locally Recoverable Quasi-Cyclic Codes Using Constituent Codes. Des. Codes Cryptogr., 2024. (Link)
A. Álvarez, M. Hunnell, J. Hutchens, E. Flapan, E. Lawrence, P. Lewis, C. Price, R. Vanderpool. Topological Symmetry Groups of the Generalized Petersen Graphs. Algebraic and Geometric Topology. 2025. (Link)
A. Álvarez, G. Heier, F. Zheng. On projectivized vector bundles and positive holomorphic sectional curvature. Proc. Amer. Math. Soc. 146, no. 7, 2877–2882, 2018. (Link)
A. Álvarez, M. Espanol, A. Faridani, C. Flores, A. Marr, E. Newman, J. McNulty, R. Nugent, A. Seneres, M. Shott, W. Y. Velez, E. Walker. The PCMI workshop for mentors: A weeklong workshop on diversity. Notices of the AMS , May 2018 (Link)
A. Álvarez. On the positive holomorphic sectional curvature of projectivtized vector bundles over compact complex manifolds. Ph.D. Dissertation, 2016.
A. Álvarez, A. Chaturvedi, G. Heier. Optimal pinching for the holomorphic sectional curvature of Hitchin’s metrics on Hirzebruch surfaces. Contemp. Math., 654:133–142, 2015. (Link)
Writing Contributions to the Profession:
A. Álvarez. Reflections: Teaching Future Elementary School Teachers via Zoom. The Seaway Current: The Official Newsletter of the MAA Seaway Section, Volume 43 - Number 04, June 2020. (Link)
Selected Grants Awarded:
July 2025: Mathematical Congress of the Americas (MCA) 2025 Travel Grant (funded by NSF Award #2420393 to the AMS)
July 2023 - [July 2026]: AMS-Simons Research Enhancement Grants for Primarily Undergraduate Institution (PUI) Faculty Grant, PI
July 2024 - July 2025: MAA Tensor Women and Mathematics Grant (Renewal), PI
July 2023 - July 2024: ERAU Faculty Innovative Research in Science and Technology (FIRST) Grant, Co-PI
July 2023 - July 2024: MAA Tensor Women and Mathematics Grant (Renewal), Co-PI
January 2023 - May 2023: ERAU Center for Teaching and Learning Excellence, Innovative Teaching Grant
July 2022 - July 2023: MAA Tensor Women and Mathematics Grant, PI
June 2019 - June 2020: SUNY Office of Diversity, Inclusion, and Equity Grant
Invited Talks:
[April 2026]: School of Mathematical and Statistical Sciences Professional Development Seminar, Arizona State University, Invited Speaker
[March 2026]: 2026 AMS Spring Southeastern Sectional Meeting - Special session on Coding Theory and its Applications to Quantum Error-Correction and Cryptography, Georgia Southern University
January 2026: Center for Teaching & Learning Excellence, Teaching Innovation Exchange (TIE) Showcase, ERAU Daytona Beach, Keynote Speaker
October 2025: 2025 AMS Fall Southeastern Sectional Meeting - Special Session on Special Session on Cryptography, Coding Theory, and their Intersections with Algebraic Geometry & Combinatorics, Tulane University
July 2025: 2025 Mathematical Congress of the Americas - Session on Network Coding and Related Fields, Miami, FL
March 2025: 2025 AMS Spring Southeastern Sectional Meeting - Special Session on Coding Theory for Modern Applications, Clemson University
January 2025: The 2025 Joint Math Meetings - AMS Contributed Paper Session on Operations Research, Game Theory, Economics, Information and Control, Seattle, WA
August 2024: 2024 MAA MathFest - MAA Invited Paper Session on Research and Career Journeys from the Project NExT Beautiful Blues '17
May 2023: Mathematical Pathways to an Excellent Future, UC Riverside (Plenary Speaker)
May 2023: 2023 AMS Spring Western Sectional Meeting - AMS Special Session on Women in Math, Fresno State U.
November 2022: Department of Mathematics Colloquium, Dnipro National University, Dnipro, Ukraine
August 2022: The Eighth Annual Conference for the Exchange of Mathematical Ideas, ERAU Prescott
April 2022: ArizMATYC/MAA Southwestern Section Joint Conference, Arizona State U. Polytech
February 2022: Latinx Mathematicians Research Community (LMRC) Colloquium
December 2021: Embry-Riddle Aeronautical University Prescott Math Club
April 2021: Mathematics Colloquium, Appalachian State University
October 2020: Panel/Workshop: Coordinating Groupwork Remotely, MAA Seaway Section
October 2019: Math Alliance Speaker Series, SUNY Potsdam
March 2019: 2019 AMS Spring Central & Western Joint Sectional Meeting - AMS Special Session on Topics on the Interface of of Analysis and Geometry, U. Hawaii
April 2018: Minorities In Mathematics Speaker Series (MIMSS), West Point - United States Military Academy
January 2018: The 2018 Joint Math Meetings – AMS Special Session on Presentations by Scholars in the National Alliance for Doctoral Studies in the Mathematical Sciences, San Diego, CA
November 2017: Math Alliance: 2017 National Field of Dreams Conference, St. Louis, MO
April 2017: PDE and Differential Geometry Seminar, U. Connecticut
March 2017: UConn Math Club, U. Connecticut
January 2016: The 2016 Joint Math Meetings – AMS Special Session on Geometry and Differential Geometry, Seattle, WA
September 2015: STEM Faculty Launch Research Talk, Worcester Polytechnic Institute
October 2014: 2014 AMS Fall Western Sectional Meeting – AMS Contributed Talk, San Francisco State U.
August 2014: Pure Mathematics Topology and Geometry Seminar, U. Waterloo
September 2014: AMS Graduate Student Reading Seminar, U. Houston
April 2014: AMS/SIAM Graduate Student Paper Presentations, U. Houston
March 2014: Seminar on Complex Geometry & Complex Analysis, U. Houston
April 2013: Seminar on Complex Geometry & Complex Analysis, U. Houston
April 2012: Seminar on Complex Geometry & Complex Analysis, U. Houston
March 2011: Pi Mu Epsilon Undergraduate Research Presentation, U. Houston
Summer Programs and Workshops:
[April 2026]: Workshop on Combinatorial Coding Theory, American Institute of Mathematics, Participant
June 2025: AIM’s SQuaREs Research Program, American Institute of Mathematics, Pasadena, CA
June 2025: Collaborate@ICERM, Institute for Computational and Experimental Research in Mathematics, Providence, RI
October 2024: SIAM Quantum Intersections Convening, Tysons, VA
July 2024: Collaborate@ICERM, Institute for Computational and Experimental Research in Mathematics, Providence, RI
June 2024: AIM’s SQuaREs Research Program, American Institute of Mathematics, Pasadena, CA
July 2023: MAA Open Math Summer Workshop: Engaging Multivariable Calculus Students using CalcPlot3D and 3D-Printed Surfaces {Virtual}
July 2023: Summer Research in Mathematics (Invited Researcher), Simons Laufer Mathematical Sciences Institute
August 2022: C.O.U.R.A.G.E. (Challenging, Operationalizing, and Understanding Racialized and Gendered Events) in Undergraduate Mathematics Workshop, {Virtual}
July 2022: Deep Teaching Residency (DTR) Faculty Development Program, HHMI
July 2022: Lean for the Curious Mathematician 2022 Workshop, ICERM
September 2021: Embodied Mathematical Imagination and Cognition: Professional Development for Undergraduate Mathematics Instructors, Colorado State University {Virtual}
June 2021: Latinx Mathematicians Research Community (LMRC), American Institute of Mathematics {Virtual}
{July 2020}: Undergraduate Faculty Research Program, IAS &PCMI - postponed due to COVID-19
July 2020: Online Pedagogy: Design for Online Learning Week-long Course, SUNY Potsdam
June 2019: R.E.U.F. Continuation at the Institute for Computational and Experimental Mathematics (ICERM), Providence, RI
June 2018: Academy of IBL, MAA Carriage House Workshop, Washington, D.C.
June 2018: R.E.U.F. at American Institute of Mathematics (A.I.M.), San Jose, CA
June 2017: Workshop on Increasing Minority Participation in Undergraduate Mathematics, PCMI, Park City, UT
October 2016: NES MAA Workshop: Teaching Calculus Now, St. Michael's College, VT
September 2015: STEM Faculty Launch, Worcester Polytechnic Institute
July 2015: The Graduate Student Bootcamp for the 2015 Summer Research Institute on Algebraic Geometry, U. Utah
May 2015: Women and Math Program, “Aspects of Algebraic Geometry”, Institute for Advanced Study & Princeton U.
March 2015: Workshop for Underrepresented Groups in Academia, IMA & U. Minnesota
Conferences Attended:
October 2025: 2025 AMS Fall Southeastern Sectional Meeting, Tulane University
July 2025: 2025 Mathematical Congress of the Americas, Miami, FL
March 2025: 2025 AMS Spring Southeastern Sectional Meeting, Clemson University
January 2025: 2025 Joint Mathematics Meetings, Seattle, WA
September 2024: The 2024 Arizona Women's Symposium in Mathematics (AWSiM III) - Northern Arizona University (Organizer and Co-Director)
August 2024: MAA MathFest, Indianapolis, IN
July 2024: Building Thinking Classrooms Summer Conference 2024, Phoenix, AZ
January 2024: 2024 Joint Mathematics Meetings, San Francisco, CA
November 2023: The 2023 Arizona Women's Symposium in Mathematics (AWSiM II) - Northern Arizona University (Organizer and Co-Director)
August 2023: The Ninth Annual Conference for the Exchange of Mathematical Ideas, U. of Northern Iowa
August 2023: MAA MathFest, Tampa, FL
May 2023: Mathematical Pathways to an Excellent Future, U. of California Riverside
May 2023: 2023 AMS Spring Western Sectional Meeting, Fresno State U.
November 2022: The Arizona Women's Symposium in Mathematics (AWSiM) - Embry-Riddle Aeronautical University, Prescott (Lead-Organizer and Co-Director)
August 2022: The Eighth Annual Conference for the Exchange of Mathematical Ideas, ERAU Prescott
August 2022: MAA MathFest, Philadelphia, PA
March 2022: Midwest Geometry Conference 2022, Wichita State University
March 2022: Critical Issues in Mathematics Education 2022: Initiating, Sustaining, and Researching Mathematics Department Transformation of Introductory Courses for STEM Majors, Mathematical Sciences Research Institute
April 2022: ArizMATYC/MAA Southwestern Section Joint Conference, Arizona State U. Polytech
February 2022: Texas Geometry & Topology Conference 2022, University of Texas at Dallas
April 2019: MAA Seaway Section Meeting, St. John Fisher College
March 2019: AMS Spring Central & Western Joint Sectional Meeting, U. Hawaii at Manoa
January 2019: 2019 Joint Math Meetings, Baltimore, MD
August 2018: MAA MathFest, Denver, CO (Project NExT Fellow)
April 2018: MAA Seaway Section meeting, SUNY Brockport
February 2018: The 2018 Texas Geometry and Topology Conference, U. Houston
January 2018: 2018 Joint Math Meetings, San Diego, CA (Project NExT Fellow)
November 2017: Math Alliance: 2017 National Field of Dreams Conference, St. Louis, MO
October 2017: MAA Seaway Section/NYSMATYC Meeting, SUNY Broome
July 2017: MAA MathFest, Chicago, IL (Project NExT Fellow)
April 2017: Algebraic Geometry Northeastern Series 2017, Stony Brook U.
March 2017: Georgia Algebraic Geometry Symposium 2017, U. Georgia
January 2016: 2016 Joint Math Meetings, Seattle, WA
July 2015: 2015 Summer Research Institute on Algebraic Geometry (Week 1), U. Utah
April 2015: Texas Algebraic Geometry Symposium 2015, Texas A&M U.
February 2015: 51st Annual Texas Geometry & Topology Conference, U. Houston
January 2015: 2015 Joint Math Meetings, San Antonio, TX
October 2014: 2014 AMS Fall Western Sectional Meeting, San Francisco State U.
April 2013: 11th Annual Graduate Student Topology & Geometry Conference, U. Notre Dame
September 2012: The Topology of Algebraic Varieties, CRM at U. Montreal
April 2012: Texas Algebraic Geometry Symposium 2012, Texas A&M U.
February 2012: 47th Annual Texas Geometry & Topology Conference, U. Houston
October 2010: National Alliance Field of Dreams Conference, U. Iowa