Talks

Numbers:

Total number of talks: 39.
Number of talks as plenary/invited speaker: 4.
Number of talks by invitation (in conferences where all the talks were by invitation): 11.
Number of contributed talks: 24.

2025
1. Invited speaker
  
  Are your polyhedra the same as my polyhedra?
  
  Cycle “Poljudnih predavanj iz matematike,fizike in astronomije” (Popular lectures in mathematics, physics and astronomy).
  
  City Library, Kranj, SVN 🇸🇮. 30. Oct 2025.
  
  abstract Slides
  
  SLO: Ali veste, kaj je pravilni polieder? Ste ga kdaj opazili na pločniku? Veste, koliko jih sploh obstaja? Na predavanju bo predavatelj povedal zgodbo, ki se začne v stari Grčiji in se razteza vse do trenutnega stoletja. Ta zgodba se vrti okoli zgornjih vprašanj in o tem, kako so se odgovori nanja skozi različna zgodovinska obdobja spreminjali.ENG: Do you know what a regular polyhedron is? Have you ever seen one on the sidewalk? Do you know how many of them there are? In the talk, I will tell you a story, a story that starts in ancient Greece and goes all the way to this century. This story goes around the questions above and how they have had different answers across different periods of time.
2. Contributed
  
  Symmetries of voltage operations on maniplexes and polytopes
  
  Workshop “Graphs Embeddings and Maps on Surfaces 2025” (GEMS 2025).
  
  Hotel Slovakia, Trenčianske Teplice, SVK 🇸🇰. 26. Jun 2025.
  
  abstract Slides
  
  A classical result in the theory of maps on surfaces states that the medial of a regular map has two orbits on flags (e.g., it has two types of faces). If the original map is self-dual, however, its medial is regular — it admits symmetry that is somewhat unexpected. This prompts a natural analogue for truncation: what is the symmetry-type of the truncation of a given (say, regular) map? What conditions on the original map guarantee or forbid the emergence of unexpected symmetries for its truncation? Although the answer is known, it is less intuitive than in the medial case. In joint work with Hubard and Mochán, we introduced the notion of voltage operations, which generalise many classical operations on maps and polyhedra to the broader setting of maniplexes and abstract polytopes. In this talk, I will revisit voltage operations and present some results and ideas concerning the central question: when does an operation yield a result with unexpected symmetry?
2024
1. Contributed
  
  Vertex trantisive graph with (very) small movement
  
  Conference “Symmetries of Discrete Objects” (SODO).
  
  University of Auckland, Auckland, NZL 🇳🇿. 13. Feb 2024.
  
  abstract Slides
  
  The motion of a graph is defined as the smallest number of vertices that are not fixed by a non-trivial automorphism. In the talk we will show a classification of the vertex transitive graphs whose motion is a prime number or a (very)small integer. We shall also explore how this problem connects with some classical permutation groups and graph theory problems.
2023
1. By invitation
  
  No me amenaces... no me amenaces (con que ya son todos)
  
  Math seminar FisMat UMSNH.
  
  Faculty of Mathematics and Physics, UMSNH, Morelia, Mich. MEX 🇲🇽. 12. Nov 2023.
  
  abstract Slides
  
  Existen exactamente 5 poliedros regulares: los Sólidos Platónicos. Para muchos de nosotros éste es uno de los teoremas que más pronto aprendimos en nuestra formación y, con un poco de suerte, hasta lo demostramos. Es más, este teorema constituye el clímax del último libro de Los Elementos de Euclides... pero... ¿Sí?... En la platica vamos a analizar un poquito este famoso teorema y sobre todo, platicaremos algo de historia al respecto.
2. Contributed
  
  Cayley extensions of maniplexes and polytopes
  
  10th Slovenian Conference on Graph Theory (SiCGT).
  
  Hotel Kompas, Kranjska Gora, SVN 🇸🇮. 20. Jun 2023.
  
  abstract Slides
  
  A map on a surface whose automorphism group has a subgroup acting regularly on its vertices is called a Cayley map. Cayley extensions are a generalisation of that notion to maniplexes and polytopes. We define M to be a Cayley extension of K if the facets of M are isomorphic to K and if some subgroup of the automorphism group of M acts regularly on the facets of M. We will show that many natural extensions in the literature on maniplexes and polytopes are in fact Cayley extensions. We will also describe several universal Cayley extensions and examine the possibilities for their symmetry type graph.
2022
1. By invitation
  
  Voltage operations on maniplexes, maps and polytopes
  
  Discrete Mathematics Seminar (UL FMF).
  
  Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, SVN 🇸🇮. 15. Nov 2022.
  
  abstract
  
  Geometrical operations such as truncation, duality, Petrie-duality, among others, arise naturally in the study of highly symmetric convex polyhedra. Often these operations do not generalise in an obvious way to combinatorial objects (such as abstract polytopes). In the talk we shall present a way to deal with many of these operations in a graph-theoretical setting using maniplexes, which are combinatorial generalisation of maps on surfaces and convex polytopes. We shall see how we could potentially use these operations to build maniplexes (or abstract polytopes) with prescribed symmetry type.ˀ
2. By invitation
  
  Voltage operations on maniplexes, maps and polytopes
  
  Mathematics research seminar (UP-FAMNIT).
  
  FAMNIT, University of Primorska, Koper, SVN 🇸🇮. 14. Nov 2022.
  
  abstract Slides
  
  Geometrical operations such as truncation, duality, Petrie-duality, among others, arise naturally in the study of highly symmetric convex polyhedra. Often these operations do not generalise in an obvious way to combinatorial objects (such as abstract polytopes). In the talk we shall present a way to deal with many of these operations in a graph-theoretical setting using maniplexes, which are combinatorial generalisation of maps on surfaces and convex polytopes. We shall see how we could potentially use these operations to build maniplexes (or abstract polytopes) with prescribed symmetry type.
3. By invitation
  
  Extensiones de politopos áltamente simétricos (Extensions of highly symmetric polytopes)
  
  Colloquium of the Institute of Mathematics (IM-UNAM).
  
  Institute of Mathematics, UNAM, Mexico City, MEX 🇲🇽. 5. Apr 2022.
  
  abstract Slides
  
  Un cubo puede ser pensado como una familia de cuadrados pegados por sus aristas. De manera similar, la teselación de cubos del espacio puede ser pensada como una familia de cubos pegados por sus caras cuadradas. Esta idea recursiva de construcción se puede entender no solo en el contexto de objetos geométricos como poliedros o teselaciones sino también en un contexto puramente combinatorio: el de los politopos abstractos. En la charla exploraremos una serie de problemas ligados a la pregunta: dado un politopo K de rango (dimensión) n, ¿Existe un politopo P de rango n+1 tal que todas las caras de rango n de P son isomorfas a K? De particular interés será cuando ponemos condiciones preestablecidas de simetría sobre P.
2021
1. By invitation
  
  Highly symmetric polytopes with prescribed local combinatorics
  
  Algebraic Graph Theory International Webminar.
  
  2. Mar 2021.
  
  abstract Slides
  
  Convex polyhedra and tilings of the Euclidean of hyperbolic plane can be thought as a family of polygons glued together along their edges. This idea extends to higher dimensions: a 4-dimensional cube can be thought as family of 3-dimensional cubes glued together along its 2-dimensional faces. This way of thinking polytopes gives rise to some natural questions: given a n-dimensional polytope K, can we build a (n+1)-dimensional polytope P such that all the facets (maximal proper faces of P) are isomorphic to K? how many of such P can we build? Usually the geometry plays an important role on those questions.In the talk we will explore variants of this question in the context of abstract polytopes, where the geometry is less relevant. In particular, we are interested in the situation where prescribed symmetry conditions are imposed on P.
2020
1. Invited speaker
  
  Toros cuadriculados muy simétricos (Highly symmetric squared tori)
  
  Encuentro Nororiental de Matemáticas (University of Pamplona).
  
  Online for the University of Pamplona, Pamplona, COL 🇨🇴. 18. Nov 2020.
  
  Slides
2019
1. By invitation
  
  A family of regular hypertopes built from regular polytopes
  
  CMS Winter Meeting 2019.
  
  Chelsea Hotel, Toronto, ON. CAN 🇨🇦. 7. Dec 2019.
  
  abstract Slides
  
  A regular hypertope is a combinatorial object that generalises both regular hypermaps and regular polytopes. In this talk we will present a construction of a family of regular hypertopes with some preassigned conditions on their local combinatorics. This family is built from a family of regular polytopes.
2. By invitation
  
  ¿Qué ch*****os hace un matemático puro y por qué les pagamos por ello?
  
  Cycle "Tomando Ciencia".
  
  Pub Giraluna, Morelia, Mich. MEX 🇲🇽. 10. Aug 2019.
  
  Slides
3. Contributed
  
  Highly symmetric toroidal polytopes
  
  9th Slovenian Conference on Graph Theory (SiCGT).
  
  Hotel Kompas, Bled, SVN 🇸🇮. 27. Jun 2019.
  
  abstract Slides
  
  In the talk we will review a technique that has been used to classify several kinds of highly symmetric abstract polytopes lying on a toroidal ambient space. We will focus not only on the abstract approach of the classifications but on visualizing such objects.
2018
1. Contributed
  
  Extensiones quirales de toros (Chiral extensions of toroids)
  
  51th National Conferences of the Mexican Mathematical Society (SMM).
  
  Juárez Autonomous University of Tabasco, Villahermosa, Tab. MEX 🇲🇽. 23. Oct 2018.
  
  abstract Slides
  
  Un poliedro puede ser pensado como un montón de polígonos que se pegan unos con otros a través de sus aristas. Esta noción es puramente combinatoria y se extiende de manera natural a dimensiones superiores de manera recursiva, es decir, podemos pensar a los polígonos como objetos 2-dimensionales y para n > 3, hablar de objetos n-dimensionales construidos a partir de objetos (n - 1)- dimensionales. Este problema se vuelve retador cuando ciertas condiciones de simetría son impuestas. En la plática exploraremos esta situación y hablaremos brevemente sobre una construcción de este estilo para ciertas teselaciones del toro.
2. Contributed
  
  Extensiones quirales de toros (Chiral extensions of toroids)
  
  3rd National meeting of graduate students of mathematics.
  
  Centro de Ciencias Matemáticas, UNAM, Morelia, Mich. MEX 🇲🇽. 29. Aug 2018.
  
  abstract Slides
  
  Un poliedro puede ser pensado como un montón de polígonos que se pegan unos con otros a través de sus aristas. Esta noción es puramente combinatoria y se extiende de manera natural a dimensiones superiores de manera recursiva, es decir, podemos pensar a los polígonos como objetos 2-dimensionales y para n > 3, hablar de objetos n-dimensionales construidos a partir de objetos (n - 1)- dimensionales. Este problema se vuelve retador cuando ciertas condiciones de simetría son impuestas. En la plática exploraremos esta situación y hablaremos brevemente sobre una construcción de este estilo para ciertas teselaciones del toro.
3. Contributed
  
  Chiral extensions of regular toroids
  
  8th PhD Summer School in Discrete Mathematics.
  
  Hotel Planja, Rogla, SVN 🇸🇮. 3. Jul 2018.
  
  abstract Slides
  
  An abstract polytope K is an extension of an abstract polytope P if all the facets of K are isomorphic to P. Chiral polytopes are those that have all possible rotations but lack of reflectional symmetry. In the talk we will explore the problem of building chiral extensions of polytopes. We will also show a technique involving voltages over certain graphs to construct chiral extensions of regular toroids.
4. Contributed
  
  Chiral extensions of regular toroids
  
  6th Workshop "Symmetries in Graphs, Maps and Polytopes" (SIGMAP).
  
  Centro de Ciencias Matemáticas, UNAM, Morelia, Mich. MEX 🇲🇽. 26. Jun 2018.
  
  abstract Slides
  
  An abstract polytope K is an extension of an abstract polytope P if all the facets of K are isomorphic to P. Chiral polytopes are those that have all possible rotations but lack of reflectional symmetry. In the talk we will explore the problem of building chiral extensions of polytopes. We will also show a technique to build chiral extensions of regular toroids.
5. Contributed
  
  De un ejemplo con gráficas a un problema con toros (From an example with graphs to a problem on tori)
  
  33rd Colloquium “Victor Neumann-Lara” of graph theory, combinatorics and its applications.
  
  University of Havana, Havana, CUB 🇨🇺. 5. Mar 2018.
  
  abstract Slides
  
  En esta plática exploraremos con detalle una estructura de incidencia sobre \(K_{6}\). Esta construcción nos servirá para motivar un problema general de mapas con cuadrados en el toro. Finalmente, mostraremos algunos resultados relativos a este problema.
2017
1. By invitation
  
  Simetrías de toros cuadriculados (Symmetries of squared tori)
  
  Graduate students seminar CIMAT
  
  Centro de Investigación en Matemáticas (CIMAT), Guanajuato, Gto. MEX 🇲🇽. 10. Nov 2017.
  
  Slides
2. By invitation
  
  Chiral extensions of chiral polytopes
  
  3rd Conference of the Pacific Rim Mathematical Association (PRIMA).
  
  Instituto tecnólogico de Oaxaca, Oaxaca, Oax. MEX 🇲🇽. 14. Aug 2017.
  
  abstract Slides
  
  Abstract polytopes are objects that generalize convex polytopes on a combinatorial way. An elementary problem in convex polytopes is, given an n-polytope K, is there an (n + 1)-polytope P such that all the facets of P are isomorphic to K? When this problem is presented in the context of abstract polytopes it becomes interesting when symmetry conditions are imposed over P (and hence, over K). In the talk we will explain the problem with detail when both P and K are chiral polytopes. In particular we will give some results regarding the possibilities for the Schläfli type of P and some examples for small values of n.
3. Invited speaker
  
  Cubos de colores y otras cosas similares (Coloured cubes and some other similar objects)
  
  2nd Summer school of symmetries of combinatorial structures.
  
  Unidad Cuernavaca del Instituto de Matemáticas, UNAM, Cuernavaca, Mor. MEX 🇲🇽. 26. Jul 2017.
  
  Slides
4. By invitation
  
  Cubic toroids with few flag-orbits
  
  Seminar of Combinatorics and Group Theory, (UL- PEF).
  
  Faculty of Education, University of Ljubljana, Ljubljana, SVN 🇸🇮. 15. Feb 2017.
  
  Slides
2016
1. Contributed
  
  Cubos generalizados y extensiones de politopos abstractos (Generalised cubes and extensions of abstract polytopes)
  
  49th National Conferences of the Mexican Mathematical Society (SMM)
  
  University of Aguascalientes, Aguascalientes, Ags. MEX 🇲🇽. 25. Oct 2016.
  
  abstract Slides
  
  La palabra "politopo" es el término genérico para los polígonos, poliedros, etc. Los politopos abstractos generalizan de manera combinatoria a los politopos clásicos. El problema de extensión en politopos convexos consiste en determinar cuúndo un politopo de dimensión d se puede usar para construir un politopo de dimensión d+1. Este problema tiene sentido en el contexto de los politopos abstractos. En la plática veremos la importancia de este problema y ofreceremos una posible solución que generaliza una construcción clásica de los cubos.
2. Contributed
  
  Toros envolviendo esferas y otras aberraciones similares (Tori wrapping spheres and other similar aberrations)
  
  Cycle "Aquelarre Matemático 2016".
  
  Faculty of Sciences, UNAM, Mexico City, MEX 🇲🇽. 11. Oct 2016.
  
  Slides
3. Contributed
  
  Extensiones de politopos abstractos altamente simétricos (Chiral extensions of highly symmetric polytopes)
  
  2nd national meeting of graduate students of mathematics.
  
  Unidad Cuernavaca del Instituto de Matemáticas, UNAM, Cuernavaca, Mor. MEX 🇲🇽. 18. Aug 2016.
  
  abstract Slides
  
  La palabra politopo es el término genérico de la sucesión punto, segmento, polígono, poliedro... Los politopos abstractos son generalizaciones combinatorias de los politopos convexos. Un problema clásico en la teoría de politopos convexos es el siguiente: dado un politopo d-dimensional K ¿existe un politopo (d + 1)-dimensional P tal que todas las caras d-dimensionales de P son isomorfas a K? En la plática mostraremos la situación de este problema en el contexto de politopos abstractos cuando imponemos algunas restricciones de simetría en K y en P.
4. Invited speaker
  
  Toros cuadriculados y sus simetrías (Squared tori and their symmetries)
  
  16th Summer school in mathematics CCM - UNAM.
  
  Centro de Ciencias Matemáticas, UNAM, Morelia, Mich. MEX 🇲🇽. 29. Jun 2016.
  
  Slides
5. Contributed
  
  Equivelar toroids with few flag-orbits
  
  Conference “Symmetries and Covers of Discrete Objects” (SCDO).
  
  Rydges Lake Resort, Queenstown, NZL 🇳🇿. 16. Feb 2016.
  
  abstract Slides
  
  An (n+1)-toroid is a quotient of a tessellation of the n-dimensional euclidean space with a lattice group. Toroids are generalizations of maps in the torus on higher dimensions and also provide examples of abstract polytopes. Equivelar maps in the 2-torus (3-toroids) where classified by Brehem and Kühnel in 2008. In 2012 Hubard, Orbanić, Pellicer and Weiss classified equivelar 4-toroids. However, a complete classification for any dimension seems to be a very hard problem. In the talk we will present a classification of equivelar (n+1)-toroids with less than n flag-orbits; in particular, we will discuss a classification of 2-orbit toroids of arbitrary dimension.
2015
1. Contributed
  
  Teselaciones simétricas del toro n-dimensional (Symmetric tessellations of the n-dimensional torus)
  
  Cycle "Aquelarre Matemático 2015".
  
  Faculty of Sciences, UNAM, Mexico City, MEX 🇲🇽. 16. Oct 2015.
  
  Slides
2. Contributed
  
  Politopos abstractos y algunos de sus grupos (Abstract polytopes and some of their groups)
  
  Graduate students seminar CCM - UNAM.
  
  Centro de Ciencias Matemáticas, UNAM, Morelia, Mich. MEX 🇲🇽. 18. Aug 2015.
3. Contributed
  
  Simetrías: un paseo por la geometría, los mosaicos y los grupos (Symmetries: a walk through geometry, tilings and groups)
  
  Cycle "Degustaciones Matemáticas 2015"
  
  Faculty of Mathematics and Physics, UMSNH, Morelia, Mich. MEX 🇲🇽. 14. Feb 2015.
  
  Slides
2014
1. Contributed
  
  Regular polyhedra in the 3-torus
  
  5th Workshop "Symmetries in Graphs, Maps and Polytopes" (SIGMAP)
  
  Elim Conference Centre, West Malvern, GBR 🇬🇧. 7. Jul 2014.
  
  abstract Slides
  
  Since Grünbaum's paper about regular polyhedra in ordinary 3-space in the 70's, there has been a lot of work towards a classification symmetric polyhedra-like structures in several spaces. Coxeter, Schulte, McMullen and many other authors have studied symmetric tessellations of the n-dimensional torus. J. Bracho, in joint work with other authors found the regular polyhedra with planar faces in the projective space; a couple of years after, McMullen completed the list of regular projective polyhedra. In this talk we'll discuss the problem of classifying regular polyhedra in the 3-dimensional torus.
2. By invitation
  
  Poliedros regulares en el 3-toro (Regular polyhedra in the 3-torus)
  
  Graduate students seminar IM-UNAM.
  
  Institute of Mathematics, UNAM, Mexico City, MEX 🇲🇽. 1. Apr 2014.
2013
1. Contributed
  
  Poliedros regulares ¿Aún siguen de moda? (Regular polyhedra, are they still trendy?)
  
  Graduate students seminar CCM - UNAM.
  
  Centro de Ciencias Matemáticas, UNAM, Morelia, Mich. MEX 🇲🇽. 8. Nov 2013.
2. Contributed
  
  Poliedros regulares en el 3-toro (Regular polyhedra in the 3-torus)
  
  46th National Conferences of the Mexican Mathematical Society (SMM).
  
  Autonomous University of Yucatan, Merida, Yuc. MEX 🇲🇽. 28. Oct 2013.
  
  abstract Slides
  
  En los 70's Grünbaum publicó una lista de 47 poliedros regulares que compartían algunas propiedades de simetría con los sólidos platónicos. En los 80's Dress encontró un poliedro más y probó que la lista de 48 poliedros regulares en el espacio euclidiano \(\mathbb{E}^3\) es completa. En 1982 Danzer y Schulte introdujeron el concepto de politopo abstracto, concepto que generaliza a los polígonos y poliedros geométricos, rescatando su estructura combinatoria. En los 90's McMullen y Schulte prueban, partiendo de este concepto, que las lista de Grünbaum y Dress es completa. Una vez resuelto el problema en el espacio euclidiano es natural preguntarse qué pasa en otros espacios. En la platica abordaremos el problema para el 3-toro \(\mathbb{T}^{3}_{\Lambda}:= \mathbb{E}^{3}/\Lambda\) donde \(\Lambda\) es un grupo generado por 3 traslaciones linealmente independientes.
3. Contributed
  
  Poliedros regulares en el 3-toro (Regular polyhedra in the 3-torus)
  
  28th Colloquium “Victor Neumann-Lara” of graph theory, combinatorics and its applications.
  
  Clavijero Palace, Morelia, Mich. MEX 🇲🇽. 5. Mar 2013.
  
  Slides
2012
1. Contributed
  
  Poliedros regulares en pantalla de videojuegos (Regular polyhedra on a video games screen)
  
  Discrete math seminar FisMat UMSNH
  
  Faculty of Mathematics and Physics, UMSNH, Morelia, Mich. MEX 🇲🇽. 10. Nov 2012.
  
  Slides
2. Contributed
  
  Coloración en gráficas infinitas (Colorings of infinite graphs)
  
  Discrete math seminar FisMat UMSNH
  
  Faculty of Mathematics and Physics, UMSNH, Morelia, Mich. MEX 🇲🇽. 15. May 2012.
  
  Slides
2011
1. Contributed
  
  Permutaciones: ¿Funciones biyectivas o simples revolturas? (Permutations: bijections or just jumbles?)
  
  45th National Conferences of the Mexican Mathematical Society (SMM).
  
  Autonomous University of San Luis Potosí, San Luis Potosi, SLP. MEX 🇲🇽. 12. Oct 2011.
  
  abstract Slides
  
  Dado un conjunto A con n elementos, las permutaciones de los elementos de dicho conjunto tienen dos grandes formas de estudio: Una de ellas es como objetos de carácter combinatorio, muy útiles para resolver variados problemas de conteo relacionados con la idea de revolver los elementos de A. Otra forma de pensar las permutaciones son como funciones biyectivas de A en sí mismo, lo cual nos lleva a trabajar las permutaciones como objetos algebraicos, de manera más específica, como elementos del grupo \(S_n\) lo que nos permite utilizar la fortaleza del álgebra en la solución de problemas. En la plática plantearemos problemas que, en principio, son de naturaleza combinatoria y no involucran la estructura algebraica de las permutaciones; sin embargo, usaremos las ventajas de ver las permutaciones como objetos algebraicos para obtener soluciones a tales problemas.
2. Contributed
  
  Una forma 'barata' de garantizar triángulos en una gráfica (A 'cheap' way of guarantee triangles in a graph)
  
  27th Colloquium “Victor Neumann-Lara” of graph theory, combinatorics and its applications.
  
  Autonomous University of the State of Hidalgo, Pachuca, Hgo. MEX 🇲🇽. 11. Mar 2011.
  
  Slides
International audience
1. Contributed
  
  Symmetries of voltage operations on maniplexes and polytopes
  
  Workshop “Graphs Embeddings and Maps on Surfaces 2025” (GEMS 2025).
  
  Hotel Slovakia, Trenčianske Teplice, SVK 🇸🇰. 26. Jun 2025.
  
  abstract Slides
  
  A classical result in the theory of maps on surfaces states that the medial of a regular map has two orbits on flags (e.g., it has two types of faces). If the original map is self-dual, however, its medial is regular — it admits symmetry that is somewhat unexpected. This prompts a natural analogue for truncation: what is the symmetry-type of the truncation of a given (say, regular) map? What conditions on the original map guarantee or forbid the emergence of unexpected symmetries for its truncation? Although the answer is known, it is less intuitive than in the medial case. In joint work with Hubard and Mochán, we introduced the notion of voltage operations, which generalise many classical operations on maps and polyhedra to the broader setting of maniplexes and abstract polytopes. In this talk, I will revisit voltage operations and present some results and ideas concerning the central question: when does an operation yield a result with unexpected symmetry?

2025

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

International audience

National audience

Local audience / seminars