Recent colloquium and seminar talks              The spin-Spin-fermions model and its application to the cuprates        I. The normal state analysis and the pairing.        II. The superconducting state and the pseudogap.        Abstract: I review theoretical results for correlated electron materials that are sufficiently close to an antiferromagnatic instability that their staggered static magnetic susceptibility in the normal state is large compared to that found in a conventional Fermi liquid. I demonstrate that for such materials magnetically-mediated pairing interaction is a viable alternative to conventional phonon-mediated pairing, and leads to pairing in the $d_{x^{2}-y^{2}}$ channel. If the dominant interaction between quasiparticles is of electronic origin and, at energies much smaller than the fermionic bandwidth, can be viewed as being due to the emission and absorption of a collective, soft spin degree of freedom, the low-energy physics of these materials is accurately described by the spin-fermion model. In the absence of superconductivity, at sufficiently low temperatures and energies, a nearly antiferromagnetic Fermi liquid  described by this model is unconventional in that the characteristic energy above which a Landau Fermi liquid  description is no longer valid is not the Fermi energy, but is the much smaller  spin-fluctuation energy. For energies (or temperatures) between spin-fluctuation energy  and the Fermi energy, the system behavior is quite different from that in a conventional Fermi liquid. Importantly, it is universal in that it is governed by just two input parameters -an effective spin-fermion interaction energy that sets the overall energy scale, and a dimensionless spin-fermion coupling constant that diverges at the antiferromagnetic quantum critical point. I discuss the pairing instability cased by the spin-fluctuation exchange, and "fingerprints" of a spin mediated pairing that are chiefly associated with the emergence of the resonance peak in the spin response of a $d$-wave  superconductor. I identify these fingerprints in spectroscopic experiments on cuprates superconconductors. Finally, I discuss work in progress on  whether the pairing   of incoherent fermions  leads to a triue superconductivity or to a pseudogap phase. I argue  that this pairing actually only gives rise to the reduction of the  fermionic density of states at low energies,  but a true superconductivity requires a Fermi liquid behavior and emerges  only at a temperature which near the quantum critical point is well below the gap opening temperature.       Recent talks        I. Can superconductivity emerge out of a non Fermi liquid.        Abstract: I present my current understanding of the non-Fermi liquid and pseudogap physics in  the cuprates the frameworks of the spin fermion model. I  argue that near a magnetic quantum critical point (QCP), the  theory falls into the strong coupling regime, and the pairing predominantly involves non-Fermi liquid quasiparticles. I further argue that the pairing of incoherent fermions  leads to the reduction of the  fermionic density of states at low energies,  but a true superconductivity requires a Fermi liquid behavior and emerges  only at a temperature which near QCP is well below the gap opening temperature. I present the emerging phase diagram and discuss suggestions for experimental verifications.          II. Condensation energy and optical properties of the cuprates. October 15, 2002        Abstract: We consider the condensation energy, $E_c$ of strongly coupled, magnetically-mediated superconductors withinthe context of the spin-fermion model.  We argue that although experimentally obtained values of $E_c$ are of the same order of magnitude as would be expected from BCS theory in optimally and overdoped cuprates, this agreement is coincidental.  The actual physics behind the condensation energy is much richer.  In particular, we argue that it is vital to take both the fermionic and bosonic contributions to the condensation energy into account when considering such materials, and that it is only the sum of the two contributions, $E_c$, which has physical meaning.  Both the experimental and our theoretically calculated condensation energies exhibit a {\it decrease}with further underdoping past optimal doping, e.g. in the mid to strong coupling regime.  Below optimal doping, the physics is qualitatively different from BCS theory  as the gain in the condensation energy  is a result of the feedback on spin excitations, while the fermionic contribution to $E_c$ is positive  due to an undressing'' feedback on the fermions.  We argue that the same feedback effect accounts for a gain in the   the kinetic energy  at strong coupling.       I. Singular corrections to the Fermi liquid theory. March 4, 2003       Abstract: The issue of non-analytic corrections to the Fermi-liquid behavior is revisited. Previous studies have indicated that the corrections to the Fermi-liquid forms of the specific heat and the static spin susceptibility ($C^{FL}\propto T$, $\chi _{s}^{FL}=\mbox{const}$) are non-analytic in $D\leq 3$ and scale as $\delta C(T)\propto T^{D}$, $\chi _{s}(T)\propto T^{D-1}$, and $\chi _{s}(Q)\propto Q^{D-1}$, with extra logarithms in $D=3$ and $D=1$. It is shown that these non-analytic corrections originate from the universal singularities in the dynamical bosonic response functions of a generic Fermi liquid. In contrast to the leading, Fermi-liquid forms which depend on the interaction averaged over the Fermi surface, the non-analytic corrections are parameterized by only two coupling constants, which are the components of the interaction potential at momentum transfers $q=0$ and $q=2p_{F}$. For 3D systems, a recent result of Belitz, Kirkpatrick and Vojta for the spin susceptibility is reproduced and the issue why a non-analytic momentum dependence, $\chi _{s}(Q,T=0)-\chi _{s}^{FL}\propto Q^{2}\log Q$, is \emph{%not }paralleled by a non-analytictity in the $T-$ dependence ($\chi_{s}(0,T)-\chi _{s}^{FL})\propto T^2$ is clarified. For 2D systems, explicit forms of $C(T)-C^{FL}\propto T^{2}$, $\chi (Q,T=0)-\chi ^{FL}\propto |Q|$ and $\chi (0,T)-\chi ^{FL}\propto T$ are obtained. It is shown that earlier calculations of the temperature dependences in 2D are incomplete.