Advances in Mathematics and Applications

1. Front Matter

   Pages i-x

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2. “And Now We’re in 2018…”

   • João Frederico da Costa Azevedo Meyer

   Pages 1-7

3. Applied Mathematics in Brazil: Challenges and Opportunities

   • Martin Tygel

   Pages 9-23

4. The Biomathematics in IMECC

   • Rodney Carlos Bassanezi

   Pages 25-65

5. Phase Field: A Methodology to Model Complex Material Behavior

   • José Luiz Boldrini

   Pages 67-103

6. Spherical Codes from Lattices

   • Sueli I. R. Costa, João E. Strapasson, Cristiano Torezzan

   Pages 105-129

7. Nonvariational Semilinear Elliptic Systems

   • Djairo G. de Figueiredo

   Pages 131-151

8. Perfect Simulation and Convex Mixture of Context Trees

   • Nancy L. Garcia, Sandro Gallo

   Pages 153-178

9. Inference in (M)GARCH Models in the Presence of Additive Outliers: Specification, Estimation, and Prediction

   • Luiz Koodi Hotta, Carlos Trucíos

   Pages 179-202

10. Notes on Newton’s Method After 1960

    • José Mario Martínez

    Pages 203-218

11. Minimal Surfaces and Their Gauss Maps

    • Francesco Mercuri, Luquesio P. M. Jorge

    Pages 219-245

12. Galois Theories: A Survey

    • Antonio Paques

    Pages 247-273

13. On the Geometry and Topology of the Commutator of Unit Quaternions

    • Alcibiades Rigas, Dan A. Agüero Cerna

    Pages 275-299

14. Life in the Rindler Reference Frame: Does a Uniformly Accelerated Charge Radiate? Is There a Bell ‘Paradox’? Is Unruh Effect Real?

    • Waldyr A. Rodrigues Jr., Jayme Vaz Jr.

    Pages 301-348

15. Flag Type of Semigroups: A Survey

    • Luiz A. B. San Martin

    Pages 351-372

16. Generic Singularities of 3D Piecewise Smooth Dynamical Systems

    • Marco Antonio Teixeira, Otávio M. L. Gomide

    Pages 373-404

17. Back Matter

    Pages 403-407

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This book celebrates the 50th anniversary of the Institute of Mathematics, Statistics and Scientific Computing (IMECC) of the University of Campinas, Brazil, by offering reviews of selected research developed at one of the most prestigious mathematics institutes in Latin America. Written by senior professors at the IMECC, it covers topics in pure and applied mathematics and statistics ranging from differential geometry, dynamical systems, Lie groups, and partial differential equations to computational optimization, mathematical physics, stochastic process, time series, and more. A report on the challenges and opportunities of research in applied mathematics - a highly active field of research in the country - and highlights of the Institute since its foundation in 1968 completes this historical volume, which is unveiled in the same year that the International Mathematical Union (IMU) names Brazil as a member of the Group V of countries with the most relevant contributions in mathematics.

• mathematical research
• dynamical systems
• algebraic geometry
• Lie theory
• fuzzy systems
• Clifford algebras
• time series
• code theory
• mathematics in Brazil
• IMECC
• Unicamp

• Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, Brazil

  Carlile Lavor, Francisco A. M. Gomes

Carlile Lavor graduated in Mathematics from the University of Campinas in 1996, and received a PhD in Computer Science from the Federal University of Rio de Janeiro, in 2001. He was a visiting professor at prestigious institutions like École Polytechnique (2008-2009) and Duke University (2013-2014). Since 2005, he has been working at the University of Campinas, where he is now a full professor. His research on  distance geometry in the last 15 years culminated in the publication of a paper in SIAM Review (first published in 2014), which was awarded the Notable Article Prize from the ACM Computing Reviews in 2015. He is co-author of the book "Euclidean Distance Geometry" and co-editor of "Distance Geometry: Theory, Methods and Applications" book, both by Springer.  



Francisco de Assis Magalhães Gomes Neto is a civil engineer (University of Brasília, 1985) with a PhD in Applied Mathematics from the University of Campinas (1995). He pursued post-doc studies at the Rice University, USA (1997). Gomes is currently an associate professor at the University of Campinas, and since 2014 has been director of the Institute of Mathematics, Statistics and Scientific Computing (IMECC) at the same university. His research interests focus on topics related to non-linear programming.

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