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Research
- SO(3)-invariant Yang-Mills fields which are not self-dual (with R. Montegomery). In: Hamiltonian systems, transformation groups and spectral transform methods (Montreal, PQ, 1989), 191--198, Univ. of Montréal, Montréal QC, 1990. Harnad, J., Marsden, J.E. (eds.). Montréal: Les publications CRM 1990.
- Yang-Mills Fields which are not Self-Dual, Commun. Math. Phys. 145 (1992), 393-410.
- Symmetric Instantons and the ADHM Construction (with J. Segert), Commun. Math. Phys. 183 (1997), 183-203.
- The cannonical bundle of an hermitian manifold (with L. Hernandez), Bol. Soc. Mat. Mexicana (3) 5.1 (1999), 187-198.
- Bochner formulae for orthogonal G-structures on compact manifolds (with L. Hernandez), Diff. Geom. Appl. 15 (2001), 265-286.
- A Bochner formula for almost-quaternionic-Hermitian structures (with L. Hernandez), Diff. Geom. Appl. 21.1 (2004), 79-92.
- Orthogonal almost complex structures of minimal energy (with L. Hernandez, M. Salvai), Geom. Dedicata 127.1 (2007), 75-85.
- G2 and the 'rolling distribution' (with R. Montgomery.), Enseign. Math. 55 (2009), 157-196.
- Poincaré y el problema de N-cuerpos (with R. Montgomery), Miscelanea Mat. 58 (2014), 83-102.
- The dancing metric, G2-symmetry and projective rolling (with L. Hernandez, P. Nurowski), Trans. Amer. Math. Soc. 370(6) (2018), 4433-4481.
- Tire track geometry and integrable curve evolution (with M. Levi, R. Perline, S. Tabachnikov), Int. Math. Res. Notices, doi:10.1093/imrn/rny087 (2018).
- Testing the Domino Theory of Gene Loss in Buchnera aphidicola: The Relevance of Epistatic Interactions (with D. Martínez-Cano, A. Moya, L. Delaye), Life 8.2 (2018), 17.
- On the isometric conjecture of Banach (with L. Hernandez Lamoneda, V. Jimenez de Santiago, L. Montejano). Geom. Topol. 25.5 (2021), 2621-2642. DOI: 10.2140/gt.2021.25.2621
- Hill's equation, tire tracks and rolling cones (with M. Levi), Nonlinearity, 33.4 (2020), 1424.
- La geometría de trayectorias de bicicletas (with S. Tabachnikov), Ciencias 135 (2020).
- Bicycle paths, elasticae and sub-Riemannian geometry (with A. Ardentov, E. Le Donne, R. Montgomery, Yu. Sachkov), Nonlinearity 34.7 (2021), 4661-4683. DOI
- Left-invariant CR structures on 3-dimensional Lie groups (with H. Jacobowitz), Complex Anal. Synerg. 7, 23 (2021).
- Variations on the Tait-Kneser theorem (with C. Jackman and S. Tabachnikov), Math Intelligencer (2021). DOI
- Para-Kähler-Einstein 4-manifolds and non-integrable twistor distributions (with O. Makhmali and P. Nurowski). Geometriae Dedicata 216, 9 (2022). DOI
- Revisiting Kepler: new symmetries of an old problem (with C. Jackman). Arnold J. of Math., 12 Sept 2022 (online).
- On cusps of caustics by reflection: a billiard variation on Jacobi's Last Geometric Statement (with S. Tabachnikov). Am. Math. Monthly (21 March, 2023, online). DOI.
- Self-Backlund curves in centroaffine geometry and Lamé's equation (with M. Bialy and S. Tabachnikov). Comm. AMS 2 (2022), 232-282
- Chains of path geometries on surfaces: theory and examples (with T. Wilse). Preprint (2022). To appear in Israel J. Math.
- Bicycling geodesics are Kirchhoff rods (with C. Jackman and S. Tabachnikov), Nonlinearity 36 (2023), 3572-3602. DOI
- Dancing polygons, rolling balls and the Cartan-Engel distribution (with L. Hernandez). New York J. Math. 29 (2023) 981-1015.
Lecture notes and talks (mine and others)
- Two notes I wrote for a Seiberg-Witten seminar we had in Cimat some time ago: spin1.dvi and spin3.dvi.
- Lecture notes on Number Theory I wrote for the "Taller de Ciencia para Jóvenes"
- A note for highschool workshops about congruences
- PRIMES AND POWERS - notes for an elementry lecture on number theory (Hendrik Lenstra, 1993).
- Lecture notes on the 3 body problem (Richard Montgomery, 8-10 may 1997).
- The geometry of partial diffrential eqns (a.k.a, Cartan's method of equivalence, Robert Bryant gave here on).
- Lecture notes + video for Simon Donaldson visit to CIMAT, 2004
- Videos for talks of Meir Buzaglo visit to CIMAT, 2008
- Notes for a Functional Analysis Course (Mohammad Jabbari, 2021)
- A list of popular science talks I offer
Gallery of images and animations
Education
- Graduate/Posgrado::
- Mecánica Clásica, agto-dic 1994.
- topologia I, agto-dic 1995
- topologia I, agto-dic 1996
- topologia II, ene-jun 1997
- Geometria Riemanniana, ene-jun 1998
- Variable Compleja I, ene-jun 1999
- Teoría de Representaciones, ene-jun 2001
- Grupos de Lie, agsto-dic 2007
- Teoría de Representaciones, ene-jun 2008
- Mini-curso de introduccion a grupos de Lie, 6-8 dic, 2010
- Teoria de Morse, ago-dic, 2012
- Topolog'ia de variedades diferenciales, ene-jun, 2013
- Teoría de Representaciones, ago-dic 2013
- Fibrados, conexiones y clases caracteristicas: ene-jun 2014.
- Algebra Moderna: ago-dic 2019.
- Teoría de representaciones de grupos de Lie: ene-jun 2020.
- Differential geometry of plane curves -- Selected topics: March-April 2024.
- Undergraduate/Licenciatura:
- General
- Mecánica Clásica, escuela de verano, jul 1999
- Algebra Superior, ago-dic 1999
- Seminario de Problemas e Investigacion, ene-jul 2000
- Mecánica Clásica, ago-dic 2000
- Probabilidad y Estadística, ene-abr 2001
- Mecánica Clásica, escuela de verano, agosto 2001
- teoria de numeros , agsto-dic 2001
- teoria de conjuntos y logica matematica, agsto-dic 2002
- algebra lineal 1, ene-mayo 2003
- algebra lineal 1, agsto-dic 2003
- algebra lineal 2, ene-mayo 2004
- teoria de numeros, taller de calculo, julio 2005
- calculo 3, agsto-dic 2005
- calculo 4, feb-jun 2006
- teoria de numeros, taller de calculo, julio 2006
- calculo 3, agsto-dic 2006
- calculo 4, feb-jun 2007
- matematicas elementales y elementos de geometria, aug-dic 2008
- algebra lineal 1, ene-mayo 2009
- algebra lineal 2, ago-dic 2009
- matematicas elementales y elementos de geometria, ene-jun 2010
- algebra moderna 2, ago-dic 2010
- algebra lineal 1, ene-mayo 2011
- calculo 3, agsto-dic 2011
- calculo 3, agsto-dic 2014
- Geometría de curvas, oct 2014: Notas
- Matemáticas elementales, ago-dic 2017
- Topologia diferencial, ago-dic 2020
- Elementos de geometría, ago-dic 2021
- Geometría diferencial de curvas en el plano, 5-9 jun 2023
- Pre-university
- Ciencia para Jóvenes
Science workshops for highschool students that I started in the summer of 1997, then extended also for primary and middle schools - 1997: 2 math workshops for middle school (secundaria) kids: Guanajuato , Dolores Hidalgo .
- 1997: VIBA
a workshop for highschool (preparatoria) kids from rural areas of the state of Guanjuato - 2000: Proyecto Post-Primaria de CONAFE
Workshops for teachers of middle schools ("post-primaria") in rural areas of the state of Guanajuato. - 2005: Fisica 3
An ordinary physics class in a local hi-school (la preparatoria Oficial de la UG) - 2005: Chiapas
A visit to the state of Chiapas with science lectures and workshops - 2006: semana de la ciencia en Chiapas
Summer science workshops for hischool students in the the state of Chiapas, similar to the ones in Cimat - 2011: Matematicas 5 en el CIMAT
Una opcion para alumnos de nivel preparatoria de llevar un curso curricular en matematicas en el CIMAT. - 2012: Calculo en el CIMAT, ene-jun 2012
Para alumnos de nivel preparatoria (6o semestre) - 2012: Calculo en el CIMAT, ago-dic 2012
Para alumnos de nivel preparatoria (5to semestre) - 2013: Calculo integral , ene-jun 2013
Para alumnos de nivel preparatoria (6to semestre) - 2013: Algebra I, ago-dic 2013
Para alumnos de nivel preparatoria (1er semestre) - 2014: Algebra II, ene-jun 2014
Para alumnos de nivel preparatoria (2do semestre) - 2014: Algebra I, ago-dic 2014
- 2015: Algebra II, ene-jun 2015
- 2015: Algebra I, ago-dic 2015
- 2016: Algebra II, ene-jun 2016
- 2016: Geometria y trigonometria, ago-dic 2016
- 2017: Geometria Analitica, ene-jun 2017
- 2017: Geometria y trigonometria, ago-dic 2017
- 2018: Geometria Analitica, ene-jun 2018
- 2018: Algebra I, ago-dic 2018
- 2019: Algebra II, ene-jun 2019
- 2019: Algebra I, ago-dic 2019
- 2020: Algebra II, ene-jun 2020
- 2020: Algebra I, ago-dic 2020
Vita
- 1957: born, Israel.
- 1983: B.A., Math+Physics, Hebrew U., Jerusalem.
- 1985: M.A, Math, Hebrew U., Jerusalem.
- 1991: Ph.D. , Univ. of California, Berkeley ("Yang Mills Fields which are not self-dual").
- 1991-4: Post-doc, Univ. of Arizona, Tucson.
- 1994-present: CIMAT, Guanajuato, Mexico.
- Citizenship: Mexico, Israel.
- Math interests: differential geometry, mathematical physics, (mostly).
- Other interests: woodworking, music, ...
Amusement (my kind)
- Beautiful science lectures
- Solar Graph for Guanajuato
- Things in Java.
- Immunoglobulin (animated jif, about 250K). Some kind of protein, I think. Dowloaded from http://www.umass.edu/microbio/rasmol/.
- imrot shefer (also this)
- some view
- special html symbols; more symbols
- Latex math symbols (PDF)
- A woodworkers puzzle, The solution
- An optical effect (needs Windows. Click on the icon and stare on the center of the screen for 30 seconds. Then look at yr hand on the mouse. Dont scream).
- an annoying optical ilussion.
- Rotation (to stop the rotation look at a single point for a while). More here, or here.
- Elephant
- A yidish parrot,
- Another parrot joke,
- Anecdote: English, spanish
- Nothing
- Incompetent design
- on teaching math to kids,
- A topological puzzle | solution
- Tokyo water park,
- World Map
- Condi + George
- Transverse Mercator Calculator (also a spanish version)
- Sudoku:1, 2
- Scott Kim
- scale
- Grucho }8-)>
- El Orito (si este no funcina intente aqui)
Some Links I like
- Woodwork
- Science
- LiE. (local: ssh to trufa and the command "lie". Manual: DVI, Postscript, PDF.) )
- SCIENCE HOBBYIST
- Penrose tilings: QuasiTiler 3.0, A Java Applet
- Planks a neat maze-type puzzle (more goods here)
- Video of a lecture on soap bubbles (in hebrew, dont let it bother you)
- Wonders of Physics (see the videos)
- Health
- ASK DR STOLL (a discussion group)
- Traute's Homepage (pretty interesting ideas and views on health)
- Politics
Bye :-)
- Ciencia para Jóvenes
