# Welcome

The term ''geometric algebra'' has been introduced most of all with respect to the second book of Euclid's Elements, where geometrical techniques were proved by many 'algebraic' properties, and by which quadratic equations were solved. In geometric algebra, all the magnitudes are geometrically represented: numbers as segments, products as rectangles, without distinctions between the geometric entities and their numerical magnitudes. Here, equality means ''equal measure''. Mathematically, a geometric algebra is defined as the Clifford algebra of a vector space with a quadratic form. Clifford's contribution was to define a new product, the geometric product, that united the Grassmann and Hamilton algebras into a single structure. A Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. Clifford algebras generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal transformations. Clifford algebras have important applications in a variety of fields including geometry, theoretical physics and digital image processing.

In 2016, the first edition of the Alterman Conference was held at the Transilvania University of Brasov (Romania), while the 2017 Alterman Summer School was held at the University of Architecture, Civil Engineering and Geodesy in Sofia (Bulgaria), and the third edition of the Alterman conference was held at Politecnico di Milano University, Italy. The 4th Alterman Conference will take place at Manipal Institute of Technology (MIT), Manipal Academy of Higher Education (MAHE) (Deemed to be University) organized by the Department of Mathematics, MIT, Manipal. The conference is partially sponsored by Eric Alterman.

The main objectives of the 2019 Alterman Conference-cum-workshop are:

- To discuss new ideas, share results and identify new trends in Computational aspects of algebra, Geometric Algebra. Dissemination of recent research papers on these topics are planned. The conference component will also have talks on computational aspects of algebra.
- To facilitate early researchers a workshop is planned. The workshop will focus on Kähler Calculus with special sessions on Clifford Algebra, Operator Algebra, and Non-Linear Algebraic Structures.

#### Past Alterman Conferences:

- 2016 Alterman Conference, August 2016 Romania. - http://cs.unitbv.ro/~acami/
- 2017 Alterman Conference, July 2017 Bulgaria. - https://altermanschool2017.uacg.bg/
- 2018 Alterman Conference, July 2018 Italy. - http://www.2018altermanconference.polimi.it/

#### Past Conferences organized by Department of Mathematics, MIT Manipal:

- National Workshop: Computer Applications based on Modern Algebra, Jan 2013 held at Manipal Institute of Technology, Manipal, India (sponsored by NBHM, DST, DRDO, CSIR and INFOSYS).
- 24th International Conference on Nearrrings, Nearfields and Related Topics, July 2015, held at Manipal Institute of Technology, Manipal, India (sponsored by DST, DRDO, ISRO and KSTA).
- 2nd National Workshop-cum-Conference: Computer Applications based on Modern Algebra, July 2017, held at Manipal Institute of Technology, Manipal, India (sponsored by DST, NBHM, INSA, CSIR, and ISRO).